1)Suppose thatxhas a binomial distribution withn= 202 andp= 0.47.

Make continuity corrections for each of the following, and then use the normal approximation to the binomial to find each probability:

P (x = 83)

P (x 99)

P (x < 73)

P (x 100)

P (x > 104)

2)An apple juice producer buys all his apples from a conglomerate of apple growers in one northwestern state. The amount of juice obtained from each of these apples is approximately normally distributed with a mean of 2.25 ounces and a standard deviation of .15 ounce. Between what two values (in ounces), symmetrically distributed around the population mean, will 80 percent of the apples fall?

3)A tire company has developed a new type of steel-belted radial tire. Extensive testing indicates the population of mileages obtained by all tires of this new type is normally distributed with a mean of 36,483 miles and a standard deviation of 3,734 miles. The company wishes to offer a guarantee providing a discount on a new set of tires if the original tires purchased do not exceed the mileage stated in the guarantee. What should the guaranteed mileage be if the tire company desires that no more than 2 percent of the tires will fail to meet the guaranteed mileage?