A company that has a large number of supermarket grocery stores claims that customers who pay by personal checks spend an average of $87 on groceries at these stores with a standard deviation of $22. Assume that the expenses incurred on groceries by all such customers at these stores are normally distributed.
a. Find the probability that a randomly selected customer who pays by check spends more than $114 on groceries.
b. What percentage of customers paying by check spends between $40 and $60 on groceries?
c. What percentage of customers paying by check spends between $70 and $105?
d. Is it possible for a customer paying by check to spend more than $185? Explain.