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At a local high school with over 2,000 students, 65% of the student body participates in a school sponsored extracurricular activity. Suppose that the school newspaper is doing an article on student participation in extracurricular activities and surveys a random sample of 100 students about their participation. Let p represent the proportion of students who participate in an extracurricular activity in a sample of size 100. Why is the sampling distribution of p approximately normal? (A) Because np and n(1 - p) are both sufficiently large. (B) Because the sample was randomly selected. (C) Because the sample size is less than 10% of the population size. (D) Because the sampling distribution of a sample proportion is always approximately normal. (E) The sampling distribution of p is not approximately normal because the survey question has only two possible answers, and a binary variable cannot be approximately normally distributed.

At a local high school with over 2,000 students, 65% of the student body participates in a school sponsored extracurricular activity. Suppose that the school newspaper is doing an article on student participation in extracurricular activities and surveys a random sample of 100 students about their participation. Let p represent the proportion of students who participate in an extracurricular activity in a sample of size 100. Why is the sampling distribution of p approximately normal? (A) Because np and n(1 - p) are both sufficiently large. (B) Because the sample was randomly selected. (C) Because the sample size is less than 10% of the population size. (D) Because the sampling distribution of a sample proportion is always approximately normal. (E) The sampling distribution of p is not approximately normal because the survey question has only two possible answers, and a binary variable cannot be approximately normally distributed.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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At a local high school with over 2,000 students, 65% of the student body participates in a school sponsored extracurricular activity. Suppose that the school newspaper is doing an article on student participation in extracurricular activities and surveys a random sample of 100 students about their participation. Let p represent the proportion of students who participate in an extracurricular activity in a sample of size 100. Why is the sampling distribution of p approximately normal? (A) Because np and n(1 - p) are both sufficiently large. (B) Because the sample was randomly selected. (C) Because the sample size is less than 10% of the population size. (D) Because the sampling distribution of a sample proportion is always approximately normal. (E) The sampling distribution of p is not approximately normal because the survey question has only two possible answers, and a binary variable cannot be approximately normally distributed.
Transcribed Image Text:At a local high school with over 2,000 students, 65% of the student body participates in a school sponsored extracurricular activity. Suppose that the school newspaper is doing an article on student participation in extracurricular activities and surveys a random sample of 100 students about their participation. Let p represent the proportion of students who participate in an extracurricular activity in a sample of size 100. Why is the sampling distribution of p approximately normal? (A) Because np and n(1 - p) are both sufficiently large. (B) Because the sample was randomly selected. (C) Because the sample size is less than 10% of the population size. (D) Because the sampling distribution of a sample proportion is always approximately normal. (E) The sampling distribution of p is not approximately normal because the survey question has only two possible answers, and a binary variable cannot be approximately normally distributed.
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