Answer:
x = the unknown number. Its square is x2. The sum of a number and its square is 12:
x + x²= 12
Putting the quadratic into standard form:
x2 + x - 12 = 0
(x+4)(x-3) = 0
x = -4 and 3
Let's check x=-4:
x + x2 = 12
(-4) + (-4)2 = 12
-4 + 16 = 12
12 = 12
Now let's check x= 3:
x + x2 = 12
3 + 32 = 12
3 + 9 = 12
12 = 12
Yup, they both work. There are two answers, x = -4 and x = 3
Find the measure of the missing angle.
Answer:
43 degrees.
Step-by-step explanation:
Since we have a box on the angle, we know that the sum of these angles is 90 degrees. These are complementary angles.
Here is a equation
x + 47 = 90
subtract 47
x = 43.
you have an srs of 23 observations from a large population. the distribution of sample values is roughly symmetric with no outliers. what critical value would you use to obtain a 98% confidence interval for the mean of the population?
The Critical value to be used to gain the 98 confidence interval for the population mean is2.508 and can be determined using the t- distribution table.
critical value is the value of a test statistic that defines the upper and lower bounds of the confidence interval or determines the position of statistical significance in a statistical test.
Given
You have an SRS of 23 compliances from a large population.The distribution of the sample values is roughly symmetric, with no outliers.98% confidence interval.The following way can be carried out to determine the critical value
Step 1-First determine the degrees of freedom using the following formula
degrees of freedom = n- 1
where n is the sample size.
Step 2- Replace" n" in the below formula.
degrees of freedom = 23- 1
= 22
Step 3- Now you can use the t- distribution table to determine the critical value to get a 98 confidence interval.
critical value = 2.508
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A math class is set up to have assignments worth 45%, quizzes worth 40% and the final exam is worth the rest of the grade. If Serena has 78% on assignments and 65% on quizzes and 96% on the final, what is her overall grade to 2 decimal places?
Serena's overall grade in the course is 75.5%. It's important to note that in a weighted grading system like this, the final exam is often a major determinant of the final grade.
To calculate Serena's overall grade, we need to first determine the weight of the final exam. We know that the assignments are worth 45% and the quizzes are worth 40%, which leaves 100% - 45% - 40% = 15% for the final exam.
Next, we can calculate Serena's grade for each component of the course. Her grade for assignments is 78% and her grade for quizzes is 65%. We can calculate her grade for the final exam by multiplying her score of 96% by the weight of the final, which is 15%:
Final grade = (0.45 * 78%) + (0.4 * 65%) + (0.15 * 96%)
Final grade = 35.1% + 26% + 14.4%
Final grade = 75.5%
Therefore, Serena's overall grade in the course is 75.5%. It's important to note that in a weighted grading system like this, the final exam is often a major determinant of the final grade. In this case, Serena's strong performance on the final exam helped to boost her overall grade, even though her scores on the assignments and quizzes were not as high. It's also worth noting that this calculation assumes that all assignments, quizzes, and the final exam were weighted equally within their respective categories (i.e., each assignment was worth the same percentage of the assignment grade).
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graph
y = -6
4x + y = 2
in the number 240.149, how does the value of the 4 in the hundredths place compare to the value of the 4 in the tens place?
The 4 in the hundredths place has a smaller value than the 4 in the tens place.
In the decimal number system, each digit to the left of the decimal point represents a power of 10, starting with 10^0 = 1 for the rightmost digit. Each digit to the right of the decimal point represents a negative power of 10, with the place value decreasing as you move farther to the right.
In the number 240.149, the 4 in the tens place represents 4 x 10 = 40. The 4 in the hundredth place represents 4/100 or 0.04, which is smaller than 40. Therefore, the 4 in the tens place has a greater value than the 4 in the hundredths place.
Hence, the value of a digit in a decimal number depends on its position relative to the decimal point. Digits to the left of the decimal point represent whole numbers, while digits to the right of the decimal point represent fractions or parts of a whole.
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a searchlight is shaped like a paraboloid of revolution. if the light source is located 2 feet from the base along the axis of symmetry and the opening is 5 feet across, how deep should the searchlight be?
A searchlight is shaped like a paraboloid of revolution. if the light source is located 2 feet from the base along the axis of symmetry and the opening is 5 feet across, 2.5 feet deep should the searchlight be.
As per the given information,
A searchlight is shaped like a paraboloid of revolution. If the light source is located 2 feet from the base along the axis of symmetry and the opening is 5 feet across.
Here we have to Find: How deep should the searchlight be.
First of all, we need to find the equation of the paraboloid of revolution.
Let's assume that the axis of the paraboloid is along the y-axis and the vertex is at the origin (0, 0, 0).
So, the equation of the paraboloid is given by:
y² = 4ax
Where, a = 2 feet (distance of light source from vertex)
So, the equation of the paraboloid is:
y² = 8x ..... (1)
The opening of the paraboloid is given to be 5 feet across.
We know that the diameter of a circle is equal to twice the radius. Hence, the radius of the opening is 2.5 feet.
The vertex is the point (0, 0, 0). We need to find the depth of the searchlight. The depth is nothing but the perpendicular distance from the vertex to the plane of the opening. The plane of the opening is given by the equation x = -2.5 (since the opening is along the yz-plane)
The equation of the plane is given by x = -2.5
Now, we need to find the coordinates of the point where the paraboloid intersects the plane of the opening.
We can substitute x = -2.5 in equation (1) to get:
y² = -20
Squaring both sides, we get:
y = ±√(-20)
Since y can only be positive (since we are considering the upper half of the paraboloid),
y = √(-20) = i√20 = 2√5 i
So, the point where the paraboloid intersects the plane of the opening is (-2.5, 2√5 i, 0)
The depth is nothing but the perpendicular distance from the vertex (0, 0, 0) to the point (-2.5, 2√5 i, 0). Hence, the depth is given by:√((-2.5 - 0)² + (2√5 i - 0)² + (0 - 0)²)= √(6.25 + 20 - 0) = √26.25 = 2.5 feet
Hence, the depth of the searchlight should be 2.5 feet.
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There are 8 red cards, 6 blue cards, 7 purple cards, and 4 green cards in a hat.
Part A. What is the theoretical probability of drawing a red card from the hat?
Part B. In a trial, a card is drawn from the hat and then replaced 1,150 times. A red card is drawn 437 times. How much greater is the experimental probability than the theoretical probability?
Oh, wait- I figured it out hehe
Part A: The theoretical probability of drawing a red card is 0.32 or 32%.
Part B: The experimental probability of drawing a red card is 0.38 or 38%, and it is 6% greater than the theoretical probability.
Part A: The theoretical probability of drawing a red card from the hat is the number of red cards divided by the total number of cards in the hat:
[tex]P_{red}[/tex] = 8 ÷ (8 + 6 + 7 + 4)
= 8 ÷ 25
= 0.32 or 32%.
Part B: The experimental probability of drawing a red card can be calculated by dividing the number of times a red card was drawn by the total number of trials:
[tex]P_{red}[/tex] = 437 ÷ 1150
= 0.38 or 38%.
The difference between the experimental probability and the theoretical probability can be calculated as follows:
0.38 - 0.32
= 0.06 or 6%
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a normal distribution has a mean of 61 and a standard deviation of 14. what is the median? (enter an exact number as an integer, fraction, or decimal.)
The median of a normal distribution with a mean of $\mu$ and standard deviation of $\sigma$ is simply equal to the mean $\mu$. Therefore, for a normal distribution with a mean of 61 and a standard deviation of 14, the median is also 61.
This is because the normal distribution is a symmetric distribution, with the mean, median, and mode all located at the same point on the horizontal axis. The mean represents the center of the distribution and is also the balance point for the distribution, so half of the observations will be less than the mean and half will be greater than the mean.
Therefore, for a normal distribution with a given mean and standard deviation, we can use the mean as an estimate of the median. In this case, the mean is exactly equal to the median, so the median is 61.
It is worth noting that this property of normal distributions only holds for normal distributions, and not necessarily for other types of distributions. For example, in a skewed distribution, the mean and median may be quite different from each other.
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Let the random variable X denote the time until a computer server connects to your machine (in milliseconds), and let Y denote the time until the server authorizes you as a valid user (in milliseconds). Each of these random variables measures the wait from a common starting time and X< Y. Assume that the joint probability density function for X and Y is f(xy) = 6 × 10^(-6) exp(-0.001x-0002y) for x < y. Determine the probability that X+Y<2900 Round your answer to two decimal places (e.g. 98.765) P(X + Y < 2900) =
Therefore, the probability that [tex]X + Y < 2900 is 0.98.[/tex]
P[tex](X + Y < 2900) = 0.98.[/tex]
To calculate the probability, we need to use the joint probability density function of X and Y, given as f(xy) = 6 × 10^(-6) exp(-0.001x-0002y) for x < y.
We can then use the integral equation to solve this equation:
[tex]P(X + Y < 2900) = ∫02900∫x2900-x 6×10-6exp(-0.001x - 0.0002y)dydx[/tex]
The integral yields:
P(X + Y < 2900) = 0.98.
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A line has a slope of 0 and passes through the point (4,4). Write its equation in slope-intercept form.
Answer:The equation of a line that passes through a point is an algebraic equation. It can also be referred to as the Slope-Intercept Equation.The equation of the line that passes through the point (4, 4) and has a slope of 0 is written as: y = 4 The equation of the line through a point (x1, y1) can be represented by the algebraic equation:y = mx + cwhere:m = slopec = y - interceptFrom the question,(x1, y1) = (4, 4)m = slope = 0Substituting these values into the algebraic equation,4 = (0 x 4) + c Hence, y = 4The equation of the line that passes through the point (4, 4) and has a slope of zero is y = 4
Answer:
y=4
Step-by-step explanation:
If a line has a slope of 0, then it is a horizontal line, and all points on the line have the same y-coordinate. We are given that the line passes through the point (4, 4). Therefore, the equation of the line in slope-intercept form is:
y = b
where b is the y-coordinate of the point through which the line passes. In this case, b = 4, so the equation of the line is:
y = 4
Therefore, the equation of the line in slope-intercept form is y = 4.
(Please could you kindly mark my answer as brainliest)
Perform the indicated operation and reduce to lowest term.−16/5 ⋅ (−15/56)
By reducing −16/5 ⋅ (−15/56) in lowest term, the answer is 6/7.
To perform the indicated operation and reduce the result to lowest terms, we need to multiply the two fractions:
(-16/5) x (-15/56) = (16 x 15) / (5 x 56)
(when we multiply two negative numbers, the result is positive)
= 240 / 280
Now we can simplify this fraction by dividing both the numerator and the denominator by their greatest common factor, which is 40:
240 / 280 = (240 ÷ 40) / (280 ÷ 40) = 6/7
Therefore, -16/5 ⋅ (-15/56) = 6/7 in lowest terms.
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.. Sasha Abbott earns $62,550.00 in taxable income each year. The tax rate is 3.6%, and she takes zero deductions. How much tax does her employer withhold each year? A $2,380.50 B $2,251.80 C $2,500.40 D $1,823.20
Answer: B $2,251.80
Step-by-step explanation:
:)
Tom makes $273.60 in 6 days. How much does he make in 4 days?
Answer:
Step-by-step explanation:
$105.20
A store sells 3 T-shirts for $15
What is the cost per T-shirt?
Answer:
The cost per T-shirt $5.
the task of framing a building has been estimated to take an average of 25 days with a standard deviation of five days. what is the probability that the duration will be done within 22 days?
The probability that the duration for complete the task of framing a building will be done within 22 days is equals to the 0.32.
The normal distribution shapes like mount, therefore, it is also known as the mounted-shaped distribution. There is only one peak of the mount, that lies at the center because the distribution belongs to the family of symmetric distributions. We have a task of framing a building has been estimated.
Average or mean, μ = 25 days
standard deviations, σ = 5 days
we have to determine the probability that the duration will be done within 22 days, P( X= 20). Assuming a normal distribution, first we determine the Z-statistic or Z-Score value. Formula for Z-score is written as, Z = ( X− μ)/σ
here, X = 20, so plug all known values
=> Z = ( 20 - 25)/5
=> Z = -5/5 = - 1
The P value is defined as the probability under the assuming that no effect or no difference (null hypothesis). Using the normal distribution table, for Z = -1 , the p value, P( Z = - 1) = P( X= 20) = 0.317311.
Hence, required probability is 0.32.
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HELP, ASAP!!
The sales tax rate in Philadelphia is 8%. Sneakers sell for $129.99. Boots sell for $89.99. How much more is the tax on the sneakers than the tax on the boots?
A. The tax on the sneakers is $3.20 more than the tax on the boots.
B. The tax on the sneakers is $4.20 more than the tax on the boots.
C. The tax on the sneakers is $3.20 less than the tax on the boots.
D. The tax on the sneakers is $4.20 less than the tax on the boots.
Step-by-step explanation:
calculate the tax on an item, we need to multiply the price by the tax rate as a decimal.
For the sneakers:
Tax on sneakers = 0.08 * $129.99 = $10.40
For the boots:
Tax on boots = 0.08 * $89.99 = $7.20
The difference between the tax on the sneakers and the tax on the boots is:
$10.40 - $7.20 = $3.20
Therefore, the correct answer is (A) The tax on the sneakers is $3.20 more than the tax on the boots
Answer: A. The tax on the sneakers is $3.20 more than the tax on the boots.
Brooke has scores of 84, 72, 90, 95, and 87 on her first five quizzes. After taking the sixth quiz, Brooke’s mean score increased.
Which could be Brooke’s sixth quiz score? Select three options.
85
90
83
86
92
Answer:
90, 86, and 92 are three options
Step-by-step explanation:
engineered ace2 immunoglobulin counters murine lethal sars-cov-2 infection through direct neutralization and fc-effector activities
YES "The engineered ACE2 immunoglobulin counters murine lethal SARS-CoV-2 infection through direct neutralization and Fc-effector activities".
What is Immunoglobulin?
An Immunoglobulin is a blood protein that recognizes foreign molecules and signals the immune system to neutralize them.
Murine lethal SARS-CoV-2 is a laboratory-made strain of SARS-CoV-2 that can infect and kill mice. It is often used in research to study the virus and test potential treatments.
ACE2 is a protein found on the surface of cells that the SARS-CoV-2 virus uses to enter and infect cells.
An engineered ACE2 immunoglobulin is an artificially created version of ACE2 that is designed to bind to the virus and neutralize it. This is achieved through direct neutralization, where the ACE2 immunoglobulin binds to the virus and prevents it from entering cells.
Additionally, the ACE2 immunoglobulin has Fc-effector activities, which means it can activate other parts of the immune system to help fight the infection.
In summary, the engineered ACE2 immunoglobulin counters murine lethal SARS-CoV-2 infection through direct neutralization and Fc-effector activities. It is an artificially created protein that binds to the virus and signals the immune system to neutralize it.
Complete Question:
Does the engineered ace2 immunoglobulin counters murine lethal sars-cov-2 infection through direct neutralization and fc-effector activities?
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Caroline has a mass of 41,390,000 and her baby sister has a mass of 3,415 grams.what is their total mass 8n kilograms
The calculated total mass of Caroline in kg by the calculation below is 41,393.415 kilograms
How to determine the total mass of Caroline in kgCaroline's mass is 41,390,000 grams.
To convert grams to kilograms, we need to divide by 1000:
41,390,000 grams / 1000 = 41,390 kilograms
Caroline's baby sister's mass is 3,415 grams.
To convert grams to kilograms, we also need to divide by 1000:
3,415 grams / 1000 = 3.415 kilograms
Therefore, their total mass in kilograms is:
41,390 kilograms + 3.415 kilograms = 41,393.415 kilograms
Hence, the total mass is 41,393.415 kilograms
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help me please !!!!!
The inequality that represents the graph is Oys-3x+2. This inequality states that the y-value is greater than or equal to -3x+2.
What is graph ?Graph is a data structure that consists of nodes (also called vertices) and edges. Nodes represent entities such as people, places or objects, while edges represent the relationship between the nodes. Graphs are used to represent many different types of real-world relationships, such as social networks, transportation networks and communication networks. Graphs can also be used to solve complex problems in computer science, operations research and mathematics. Graphs provide an efficient way to store and manipulate data and can be used to represent both directed and undirected relationships.
This inequality can be interpreted as the solution set of all points that have a y-value that is at least -3x+2.
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Help open up a jewelry store, Tom borrowed money from an online lending company He took out a personal, amortized loan for 44,000, at an interest rate of 6. 25\% with monthly payments for a term of 7 years For each part, do not round any intermediate computations and round your final answers to the nearest cent necessary, refer to the list of financial formulas (a) Find Tom's monthly payment (b) Tom pays the monthly payment each month for the full term , his total amount to repay the () Tom pays the monthly payment each month for the full termfind the total amount of interest he will pay
Tom will pay a total of $13,424.20 in interest over the term of the loan.
The formula to calculate the monthly payment for an amortized loan is given by: `P = r(PV) / [1 - (1 + r)^(-n)]`Where P is the monthly payment, r is the interest rate per month, PV is the present value of the loan, and n is the number of payments or the total number of months.
Substituting the given values, we get:P = 0.0052083333 × 44,000 / [1 - (1 + 0.0052083333)^(-7×12)]P = 632.32Therefore, Tom's monthly payment is $632.32 (rounded to the nearest cent).b. Since Tom pays the monthly payment each month for the full term, his total amount to repay the loan is equal to the present value of the loan.
Therefore, the total amount to repay the loan is $44,000 (rounded to the nearest cent).c. The total amount of interest paid over the term of the loan can be calculated as the difference between the total amount repaid and the principal amount of the loan.
Therefore, the total interest paid is: Total interest paid = Total amount repaid - Principal amount of the loan Total interest paid = $57,424.20 - $44,000Total interest paid = $13,424.20
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please answer!! A rectangle is 1/3 yards long and 2/3 yards wide.
What is the area of the rectangle?
Enter your answer as a fraction in simplest form by filling in the boxes
Answer:
2/9yd²
Step-by-step explanation:
We know that area is calculated by length × width, so we will do the same here. To get the area, we must multiply 1/3 by 2/3.
1/3 × 2/3 is 2/9. So, the area of the rectangle is 2/9yd². :D
The average age at which adolescent girls reach their adult height is 16 years_ Suppose you have sample of 29 adolescent girls who are developmentally delayed, and who have an average age at which they reached their adult height of 17.8 years and sample variance of 77.4 years You want to test the hypothesis that adolescent girls who are developmentally delayed have different age at which they reached their adult height than all adolescent girls Calculate the statistic. To do this you first need to calculate the estimated standard error: The estimated standard error IS SM 1.6337 The statistic is 1.10 Now suppose you have larger sample size n 91. Calculate the estimated standard error and the statistic for this sample with the same sample average and the same standard deviation as bove, but with the larger sample size. The new estimated standard error is 0.9222 The new statistic is 1.95 Note that the statistic becomes smaller becomes smaller. Use the Distributions tool to look at the distributions for different sample sizes_ To do this_ choose the Degrees of Freedom for the first sample size on the slider, and click the radio button with the single orange line_ Move the orange vertical line to the right until the number below the orange line is located on the statistic. The probability of getting that statistic or one more extreme will appear in the bubble with the orange type Now repeat the process for the other sample: Distribution Degrees of Freedom 3.0 2.0 1.0 0.0 1.0 2.0 3.0 What is the probability of getting the statistic or something more extreme for the sample size of n 29? p What is the probability of getting the statistic or something more extreme for the sample size of n 917 p The distribution is with larger n. (Hint: To best see this click the radio button in the tool with no vertical lines Slowly move the Degrees of Freedom slider from the smallest value to the largest value_ and observe how the shape of the distribution changes_
The student question is about calculating the statistics and probabilities for two different sample sizes of adolescent girls who are developmentally delayed, reaching their adult height.
For the sample size of 29 girls, the estimated standard error is 1.6337, and the statistic is 1.10. For the larger sample size of 91 girls, the new estimated standard error is 0.9222, and the new statistic is 1.95. As the sample size increases, the statistic becomes smaller.
Using the Distributions tool to determine the probability of getting the statistic or something more extreme for each sample size, you can find the probabilities (p) for each case. For the sample size of[tex]29 (n=29),[/tex] you will obtain a specific probability (p).
Similarly, for the sample size of[tex]91 (n=91)[/tex], you will get another probability (p). The distribution will change with larger sample sizes (n).
To observe the distribution changes, you can use the Degrees of Freedom slider in the tool and move it from the smallest value to the largest value. This will help you see how the shape of the distribution changes as the sample size increases.
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in the packet of mixed candies there are 2 fruit centers for every 3 caramel centers. there are 30 candies in the packet
Answer: there are 12 fruit centers and 15 caramel centers
Step-by-step explanation:
There's a roughly linear relationship between the number of times a species of cricket
will chirp in one minute and the temperature outside. For a certain type of cricket,
this relationship can be expressed using the formula T = 37+0.28c, where T
represents the temperature in degrees Fahrenheit and c represents the number of
times the cricket chirps in one minute. What could the number 37 represent in the
equation?
4
How long the cricket continues to chirp.
The expected temperature in degrees Fahrenheit if the cricket has chirped 37
times per minute.
The expected temperature in degrees Fahrenheit if the cricket has chirped o
times per minute.
The change in cricket chirps per minute for each additional degree Fahrenheit. no
The correct response is: The anticipated temperature in Fahrenheit if the cricket has not yet chirped once every minute.
what is linear equation ?Each term in the algebraic equation is either a constant or the result of a constant and one variable. Y = mx + b, where x is the independent variable, m is the slope, and b is the y-intercept, is the general form of a linear equation. Several real-world phenomena, like as the link between speed and time in a moving object and the relationship between price and quantity in economics, are modeled using linear equations.
given
The correct response is: The anticipated temperature in Fahrenheit if the cricket has not yet chirped once every minute.
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find the area, to the nearest hundredth, of a circle with a circumference of 19 centimeters. use 3.14 for pi
The area of the circle with circumference 19cm is 6.42cm²( nearest hundredth).
What is area of circle?Area of a circle is the region occupied by the circle in a two-dimensional plane. It can be determined easily using a formula, A = πr2. Where r is the radius.
The circumference of a circle is given as ;
C = 2πr
C = 9cm
therefore, 9 = 2× 3.14 × r
9 = 6.28r
r = 9/6.28
r = 1.43 cm
Area of circle = πr²
= 3.14 × 1.43²
= 6.42cm²( nearest hundredth)
therefore the area of the circle is 6.42cm²
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A human organism developing in the uterus from the ninth week until birth is called a (n) ____________.`
A human organism developing in the uterus from the ninth week until birth is called a(n) fetus.
A fetus is the term used to describe a human organism that is developing in the uterus from the ninth week of gestation until birth. During this time, the fetus undergoes significant growth and development, as all of the major organs and body systems are formed and begin to function.
The ninth week of gestation is considered a significant milestone in fetal development, as most of the critical stages of organogenesis have been completed by this time. From this point onward, the fetus primarily grows and matures in preparation for life outside of the womb.
During the remaining weeks of gestation, the fetus undergoes a number of important developmental processes, including continued brain development, growth of the nervous system, and development of the lungs and other vital organs. At the same time, the fetus also gains weight and size, and begins to develop a layer of fat that will help to regulate body temperature after birth.
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If shirts cost $16 each, and sales tax is 4.75%, what would be the total bill if you buy three shirts?
Answer:
$45.72
Step-by-step explanation:
16×3=48
48×0.0475(4.75%)=2.28. <----- tax
2.28+48=45.72
3. Some of the neighbors played a penny game. Players tossed a penny in a hole and earned that number of points. Each player tossed 3 pennies. The scores from each penny that went in a hole were added for a final score. Was it possible to get a score of 9? If so, how could it have happened?
It is not possible to get a score of 9 because 9 is an odd number.
What are numbers?
Numbers are mathematical symbols used to represent values or quantities. They are classified into different types based on their properties and can be used in different areas for counting, measuring, and solving problems.
What is meant by odd numbers?
Odd numbers are integers that are not evenly divisible by 2. They are characterized by having a remainder of 1 when divided by 2. They are expressed as 2n+1, where n is an integer. Examples are 1, 3, 5, 7, 9, etc.
Possibilities:
1.All three pennies score 1: total score is 3.
2.Two pennies score 1 and one penny scores 0: total score is 2.
3.Two pennies score 0 and one penny scores 1: total score is 1.
4.All three pennies score 0: total score is 0.
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if a study group draws 20 random samples of 15 from a population that has normal distribution, can the study group claim a normal distribution of the sample means?
Yes, the study group can claim a normal distribution of the sample means.
This is because when a group takes random samples from a population that has a normal distribution, the means of those samples will also follow a normal distribution. The reason for this is due to the Central Limit Theorem, which states that when a large enough number of samples are taken from a population, the distribution of the sample means will become more and more normal.
Since the study group is taking 20 random samples of 15 from a population with a normal distribution, it can be assumed that the means of the sample will have a normal distribution. Therefore, when the study group draws 20 random samples of 15 from a population that has a normal distribution, they can be certain that the sample means will also follow a normal distribution.
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