A random sample of 16 students in the School of Economics and Finance was taken to estimate average daily commuting time for all the students. Suppose that the population times have a normal distribution with a mean of 87 minutes and a standard deviation of 22 minutes. a) Find the probability that the average daily commuting time is fewer than 100 minutes. Also, find the probability that it is outside the range of 85 to 95 minutes.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section: Chapter Questions
Problem 27T
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A random sample of 16 students in the School of Economics and Finance was taken to estimate average
daily commuting time for all the students. Suppose that the population times have a normal distribution
with a mean of 87 minutes and a standard deviation of 22 minutes.
a) Find the probability that the average daily commuting time is fewer than 100 minutes. Also, find
the probability that it is outside the range of 85 to 95 minutes.
b) Suppose that a second independent random sample of 50 students is taken. Without doing the
calculations, explain whether the probabilities in part (a) would be higher, lower, or the same for
the second sample. Justify your answer.
Transcribed Image Text:A random sample of 16 students in the School of Economics and Finance was taken to estimate average daily commuting time for all the students. Suppose that the population times have a normal distribution with a mean of 87 minutes and a standard deviation of 22 minutes. a) Find the probability that the average daily commuting time is fewer than 100 minutes. Also, find the probability that it is outside the range of 85 to 95 minutes. b) Suppose that a second independent random sample of 50 students is taken. Without doing the calculations, explain whether the probabilities in part (a) would be higher, lower, or the same for the second sample. Justify your answer.
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