Question

Total sleep time of college students. A recent survey describes the distribution of total sleep time among college students as approximately Normal with a mean of 6.78 hours and standard deviation of 1.24 hours.3 Suppose that we select a college student at random and obtain his or her sleep time. This result is a random variable X because, prior to the random sampling, we don't know the sleep time. We do know, however, that in repeated sampling, X will have the same N(6.78, 1.24) distribution that describes the pattern of sleep time in the entire population. We call N(6.78 1.24) the population distribution. 5.28 Total sleep time of college students. In Example 5.4, the total sleep time per night among college students was approximately Normally distributed with mean 6.78 hours and standard deviation o 1.24 hours. You plan to take an SRS of size n = 120 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?

Answer 1

that Here givin 8I24 120 u= 6.18 centml As weknow th9t thexomr Limit N4,2) Averng f6 9Lrege deviahsn standard Standard I24 120 Vn StAndard devighin O.1132 CLOdia empivical rwe he datu f deiahsn Tmena. e G 2 C0.1132 1- S.S536 26 6-78 + 2. xCa1132) T. O069

of he 68- s- 99. nule fhis s9nyle part to desribe thev VArinbiliky mean is 1. o0 64) C6.5536 944 C.9- .78 1132 10601) O.855 . -060 Reguired O.855