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. Two 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 through c below.
c. If x has a binomial distribution, then so does the number, y, of balls in the sample that meet the association's minimum diameter. [Note: x + y = 24.] Describe the distribution of y. In particular, what are p, q, and n? Also, find E(y) and the standard deviation of y.
Determine the value of p for the distribution of y.
p = (Type an integer or a decimal.)
Determine the value of q for the distribution of y.
q = (Type an integer or a decimal.)
Determine the value of n for the distribution of y.
n =
Determine the expected value for the distribution of y, E(y).
E(y) = (Round to one decimal place as needed.)
Determine the standard deviation for the distribution of y, σy.
