11. The Office of Student Services at a large western state university maintains

Question

11. The Office of Student Services at a large western state university maintains information on the study habits of its full-time students. Their studies indicate tha? the mean amount of time undergraduate students study per week is 20 hours. The hours studied follows the normal distribution with a standard deviation of six hours Suppose we select a random sample of 144 current students. a) What is the probability that the mean of this sample is between 19 hours and 20 hours? b) What is the probability that the mean of this sample is between 19.25 hours and 21.0 hours? 12. A population consists of 14 values. How many samples of size five are possible? (5)

Explanation / Answer

#11.
mean = 20
sd = 6
n = 144

SE = sd/sqrt(n) = 6/sqrt(144) = 0.5

a)
P(19 < z < 20)
= P((19 - 20)/0.5 < z < 0)
= P(-2 < z < 0)
= P(z < 0) - P(z < -2)
= 0.5 - 0.0228
= 0.4772

b)
P(19.25 < z < 21)
= P((19.25 - 20)/0.5 < z < (21 - 20)/0.5)
= P(-1.5 < z < 2)
= P(z < 2) - P(z < -1.5)
= 0.9772 - 0.0668
= 0.9104

#12.
Selecting 5 from 14, this can be done in 14C5 ways

Hence number of possible samples are 14C5 = 2002

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