A general statement is made that an error occurs in 10% of all retail transactions. We wish to evaluate the truthfulness of this figure for a particular retail store, say store A. Twenty transactions of this store are randomly obtained. Assuming that the 10% figure also applies to store A and let X be the number of retail transactions with errors in the sample a. The probability distribution function (pdf) of X is binomial. Identify the parameters n and p.
b. Calculate the expected value of X.
c. Calculate the variance of X.
d. Find the probability exactly 2 transactions sampled are in error.
e. Find the probability at least 2 transactions sampled are in error.
f. Find the probability that no more than one transaction is in error.
g. Would it be unusual if 5 or more transactions were in error?