Tennyson High School (THS) is one of our local high schools in Hayward, CA. Suppose the distribution of GPAs at THS has a mean of 2.72 and a standard deviation of 0.36. Assume that GPAs at THS follow an approximately normal distribution. The national average GPA in high schools in the United States is 2.8. (a) What is the probability that a randomly selected student at THS has a GPA higher than the national average? (b) What is the probability that in a random sample of 43 students at THS, their average GPA is higher than the national average? (c) Would your method of answering (a) or (b) be affected if the distribution of GPAs were distinctly non-normal? Explain which parts could be answered the same, which could not, and how you know. Please select all statements that are true. Group of answer choices Part (a): 0.927 Part (a): 0.412 Part (a): 0.588 Part (a): The probability cannot be calculated. Part (b): 0.927 Part (b): 0.072 Part (b): 0.412 Part (b): The probability cannot be calculated. Part (c): The answer to part (a) changes. I could no longer do the calculation without the assumption of normality. The answer to part (b) does not change because the Central Limit Theorem applies. Part (c): The answers to both parts (a) & (b) change as the Central Limit Theorem applies. Part (c): The answer to part (a) does not change. The answer to part (b) changes. I could no longer do the calculation without the assumption of normality. Part (c): Neither answers to parts (a) & (b) change as the Central Limit Theorem applies.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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Tennyson High School (THS) is one of our local high schools in Hayward, CA. Suppose the distribution of GPAs at THS has a mean of 2.72 and a standard deviation of 0.36. Assume that GPAs at THS follow an approximately normal distribution.

The national average GPA in high schools in the United States is 2.8.

(a) What is the probability that a randomly selected student at THS has a GPA higher than the national average?

(b) What is the probability that in a random sample of 43 students at THS, their average GPA is higher than the national average?

(c) Would your method of answering (a) or (b) be affected if the distribution of GPAs were distinctly non-normal? Explain which parts could be answered the same, which could not, and how you know.

Please select all statements that are true.

Group of answer choices

Part (a):

0.927

Part (a):

0.412

Part (a):

0.588

Part (a):

The probability cannot be calculated.

Part (b):

0.927

Part (b):

0.072

Part (b):

0.412

Part (b):

The probability cannot be calculated.

Part (c):

The answer to part (a) changes. I could no longer do the calculation without the assumption of normality.

The answer to part (b) does not change because the Central Limit Theorem applies.

Part (c):

The answers to both parts (a) & (b) change as the Central Limit Theorem applies.

Part (c):

The answer to part (a) does not change.

The answer to part (b) changes. I could no longer do the calculation without the assumption of normality.

Part (c):

Neither answers to parts (a) & (b) change as the Central Limit Theorem applies.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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