6.14 Total sleep time of college students. In Example 6.1 (page 289), the total
ID: 3152468 • Letter: 6
Question
6.14 Total sleep time of college students. In Example 6.1 (page 289), the total sleep time per night among college students was approximately Normally distributed with mean 6.78 hours and standard deviation 1.24 hours. You plan to take an SRS of size n = 150 and compute the average total sleep time. (a) What is the standard deviation for the average time? (b) Use the 95 part of the 68-95-99.7 rule to describe the variability of this sample mean (c) What is the probability that your average will be below 6.9 hours?Explanation / Answer
(a)The standard deviation of average time is: sigma/root over n
=1.24/root over 150=0.101
(b)The 95 part of 68-95-99.7 rule tells that the 95% of the data lies within 2 standard deviations from the mean.
That is P(mu-2sigma<=x<=mu+2sigma)?0.9545
(c)For X=6.9, z=(x-mu)/sigma
=(6.9-6.78)/0.101
=1.18
Thus, P(X<6.9)=P(z<1.18)=0.8599
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