Imprints Galore buys T-shirts (to be imprinted with an item of the customer’s choice) from a manufacturer who guarantees that the shirts have been inspected and that no more than 1% are imperfect in any way. The shirts arrive in boxes of 12. Let x be the number of imperfect shirts found in any one box.
a. List the probability distribution and draw the histogram of x.
b. What is the probability that any one box has no imperfect shirts?
c. What is the probability that any one box has no more than one imperfect shirt?
d. Find the mean and standard deviation of x.
e. What proportion of the distribution is between m _ σ and m + σ
f. What proportion of the distribution is between m _ 2σ and m + 2σ
g. How does this information relate to the empirical rule and Chebyshev’s theorem? Explain.
h. Use a computer to simulate Imprints Galore’s buying 200 boxes of shirts and observing x, the number of imperfect shirts per box of 12. Describe how the information from the simulation compares to what was expected (answers to parts a–g describe the expected results).
i. Repeat part h several times. Describe how these results compare with those of parts a–g and with part h.