Problem #$1$

To avoid unpleasant surprises when the statement comes, you try to record all your credit card

transactions in a ledger. Unfortunately, you tend to neglect to record about $3\%$ of your purchases.

Suppose that last month, you had $22$ purchases on your credit card account. When the statement

arrives, you count the number of purchases you forgot to record. The random variable $x$

represents the number of unrecorded purchases in a month with $22$ transactions.

a$.$ Explain why this is a binomial experiment.

b$.$ Find the probability that you would record all $22$ purchases.

c$.$ Find the probability that at least $7$ purchases would have been unrecorded.

d$.$ Would it be unusual to find $7$ unrecorded purchases in a month with $22$ purchases? Please

justify your response using class concepts.