Full-time college students report spending a mean of 23 hours per week on academic activities, both inside and outside the classroom. Assume the standard deviation of time spent on academic activities is 3 hours. Complete parts (a) through (d) below. a. If you select a random sample of 16 full-time college students, what is the probability that the mean time spent on academic activities is at least 22 hours per week? (Round to four decimal places as needed.) b. If you select a random sample of 16 full-time college students, there is an 89% chance that the sample mean is less than how many hours per week? (Round to two decimal places as needed.) c. What assumption must you make in order to solve (a) and (b)? A. The population is uniformly distributed. B. The sample is symmetrically distributed, such that the Central Limit Theorem will likely hold. C. The population is symmetrically distributed, such that the Central Limit Theorem will likely hold for samples of size 16. D. The population is normally distributed. d. If you select a random sample of 100 full-time college students, there is an 89% chance that the sample mean is less than how many hours per week? _______

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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Full-time college students report spending a mean of

23 hours per week on academic activities, both inside and outside the classroom. Assume the standard deviation of time spent on academic activities is 3 hours. Complete parts (a) through (d) below.

a. If you select a random sample of 16 full-time college students, what is the probability that the mean time spent on academic activities is at least

22 hours per week?

(Round to four decimal places as needed.)

b. If you select a random sample of 16 full-time college students, there is an

89% chance that the sample mean is less than how many hours per week?

(Round to two decimal places as needed.)

c. What assumption must you make in order to solve (a) and (b)?

A. The population is uniformly distributed.

B. The sample is symmetrically distributed, such that the Central Limit Theorem will likely hold.

C. The population is symmetrically distributed, such that the Central Limit Theorem will likely hold for samples of size 16.

The population is normally distributed.

d. If you select a random sample of

100 full-time college students, there is an 89%

chance that the sample mean is less than how many hours per week? _______

(Round to two decimal places as needed.)

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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