Missy Walters owns a mail-order business specializing in baby clothes. Missy is

Question

Missy Walters owns a mail-order business specializing in baby clothes. Missy is confident the dollar amounts of all her orders are normally distributed or nearly so. Assume she knows the mean and standard deviation are $249 and $46, respectively, for all orders she receives.
a. Describe the sampling distribution of , where is the mean dollar-amount of an order for a sample of 10 orders.
b. What is the probability that a simple random sample of 30 orders will provide an estimate of the population mean dollar-amount of an order that is within plus or minus $10 of the actual population mean?
c. What happens to the sampling distribution of when the sample size is increased from 30 to 90? With a sample size of 90, what is the probability that will be between $239 and $259?

Explanation / Answer

a) The sampling distribution of mean dollar amount will have : i) Normal distribution if number of orders in sample, n >= 30 ii) studrnt-t distribution ( or simply referred as t-distribution), with degree of freedom , v = n-1 if n sampling distribution is a t-distribution with degree of freedom ,v = n-1 = 9 , mean = $249 and sample std. deviation , s = sigma/sqrt(n) = $ 46/sqrt(10) b) n=30 => normal distribution P ( 239

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