A research group needs to determine a 90% confidence interval for the mean repair cost for all car insurance small claims. From past research, it is known that the standard deviation of such claims amounts to $124.88.

(a) What is the critical value that corresponds to the given level of confidence? Round to two decimals and remember that critical values are defined to be positive.

(b) If the group wants their estimate to have a maximum error of $12, how many small claims should they sample? Remember to round up to the next integer.