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Download STAT 211 Homework Practice 2 Suppose a random sample of 25
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STAT 211 Homework Practice 2 Suppose a random sample of 25 skiers were asked to complete a run as quickly as they could. The amount of time required to complete the run was recorded for each skier. The population (Sample was an error in typing) mean time was 95 seconds with a standard deviation of 15 seconds. 1. Determine the mean of the sampling distribution of the sample mean The distribution of skier times, X~?(95,15) We do not know if it is normal, but, we do know that because the sample size 25>20 we are able to use the central limit theorem to find the sampling distribution of the sample mean. So, the sampling distribution of the sample mean, is N(95,3) The mean of the sampling distribution of the sample mean is 95. 2. Determine the standard deviation of the sampling distribution of the sample mean From (1), the standard deviation (or standard error) of the sampling distribution of the sample mean is 3 3. Describe the shape of the sampling distribution of the sample mean The shape of the sampling distribution of the sample mean is that of a normal distribution. Some characteristics of the normal distribution are symmetric about the mean, bell shaped, uni-modal, etc. 4. Find the probability that a randomly selected skier will complete the run in under 100 seconds P(X<100) (not x bar) P(z<1/3)=.6293 5. Find the probability that the mean completion time for a group of 25 skiers will be under 100 seconds
