Question

According to a certain golf association, the weight of the golf ball shall not be greater than 1.620 ounces (45.93 grams). The diameter of the ball shall not be less than 1.680 inches. The velocity of the ball shall not be greater than 250 feet per second. The golf association periodically checks the specifications of golf balls using random sampling. Four dozen of each kind are sampled, and if more than three do not meet size or velocity requirements, that kind of ball is removed from the golf association's approved list. Complete parts a and b.

a. What assumptions must be made in order to use the binomial probability distribution to calculate the probability that a particular kind of golf ball will be removed?

A. The experiment consists of n identical trials. There are only two possible outcomes on each trial. The probability of success can change from trial to trial. The trials are dependent.

B. The experiment consists of n identical trials. There are only two possible outcomes on each trial. The probability of success remains the same from trial to trial. The trials are independent.

C. The experiment consists of n identical trials. The number of outcomes can vary. The probability of success can change. The trials are independent.

What information must be known in order to use the binomial probability distribution to calculate the probability that a particular kind of golf ball will be removed?

A. The percentage of that kind of golf ball that meets all the requirements

B. The percentage of that kind of golf ball that meets the velocity requirements

C. The percentage of that kind of golf ball that fails to meet both the size and velocity requirements

D. The percentage of that kind of golf ball that meets the size requirements

b. Suppose 10% of all balls produced by a particular manufacturer are less than 1.680 inches in diameter, and assume that the number of such balls, x, in a sample of four dozen balls can be adequately characterized by a binomial probability distribution. Find the mean of the binomial distribution.

μ=_________________(Round to the nearest tenth as needed.)           

Find the standard deviation of the binomial distribution.

σ=________________(Round to the nearest thousandth as needed.)

Answer 1

a) B. The experiment consists of n identical trials. There are only two possible outcomes on each trial. The probability of success remains the same from trial to trial. The trials are independent.

C. The percentage of that kind of golf ball that fails to meet both the size and velocity requirements.

b)

n = 12*4 = 48

p = 0.10