Suppose certain coins have weights that are normally distributed with a mean of 5.612 g

5.612g and a standard deviation of 0.054 g

0.054g. A vending machine is configured to accept those coins with weights between 5.522

5.522 g and 5.702

5.702 g.

a. If 290

290 different coins are inserted into the vendingmachine, what is the expected number of rejectedcoins?

The expected number of rejected coins is

28

28. (Round to the nearestinteger.)

b. If 290

290 different coins are inserted into the vendingmachine, what is the probability that the mean falls between the limits of 5.522

5.522 g and 5.702

5.702 g?

The probability is approximately

nothing

. (Round to four decimal places asneeded.)