Question

The United States Golf Association requires that the weight of a golf ball must not exceed 1.62 oz. The association periodically checks golf balls sold in the United States by sampling specific brands stocked by pro shops. Suppose that a manufacturer claims that no more than 17 percent of its brand of golf balls exceed 1.62 oz. in weight. Suppose that 24 of this manufacturer's golf balls are randomly selected, and let x denote the number of the 24 randomly selected golf balls that exceed 1.62 oz. Refer to the Binomial table given below. Excel Output of the Binomial Distribution with n = 24, p = 0.17, and q = 0.83 Binomial distribution with n = 24 and p = 0.17 x P(X=x) 0 0.0114 1 0.0562 2 0.1323 3 0.1987 4 0.2137 5 0.1750 (a) Find P(x = 0), that is, find the probability that none of the randomly selected golf balls exceeds 1.62 oz. in weight.

Answer 1

we have given

n = 24, p = 0.17, and q = 0.83

since this is the case of binomial distribution where x denote the number of the 24 randomly selected golf balls that exceed 1.62 oz

P(x=0) = 24C0(0.17)0(1-0.17)24 = 0.0114

the probability that none of the randomly selected golf balls exceeds 1.62 oz. in weight is 0.0114