Suppose a random sample of n 16 observations is selected fr

Suppose a random sample of n = 16 observations is selected from a population that is normally distributed with mean equal to 105 and standard deviation equal to 13. (a) Give the mean and the standard deviation of the sampling distribution of the sample mean x. (Enter your standard deviation to two decimal places.) mean standard deviation (b) Find the probability that x exceeds 111. (Round your answer to four decimal places.) (c) Find the probability that the sample mean deviates from the population mean mu = 105 by no more than 4. (Round your answer to four decimal places.)

Solution

a)

1) 105

2) 13/sqrt(16)=13/4= 3.25

b) 0.0324

c)0.2184