Suppose certain coins have weights that are normally distributed with a mean of 5.642 g and a standard deviation of 0.075 g. A vending machine is configured to accept those coins with weights between 5.552 g and 5.732 g.

a. If 290 different coins are inserted into the vending machine, what is the expected number of rejected coins?

The expected number of rejected coins is 67

b. If 290 different coins are inserted into the vending machine, what is the probability that the mean falls between the limits of 5.552 g and 5.732 g?The probability is approximately______

. (Round to four decimal places as needed.)