The united states Golf Association requites that the weight of a golf ball must

Question

The united states Golf Association requites that the weight of a golf ball must not exceed 1 62 oz The associate 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 3 percent of its brand of god 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 03, and q = 0 97 Binomial distribution with n = 24 and p = 0 03 Find P(x = 0), that is, find the probability that none of the randomly selected god balls exceeds 1 62 oz in weight (Use table values rounded to 4 decimal places for calculations. Round your answer to 4 decimal places.) Find the probability that at toast one of the randomly selected golf bait exceeds 1 62 oz in weight (Use table values rounded to 4 decimal places for calculations. Round your answer to 4 decimal places.) Find P(x 2) (Use table values rounded to 4 decimal places tor calculations Round your answer to 4 decimal places.) Suppose that 2 of the 24 randomly selected golf balls are found to exceed 1 62 oz Using your result from part d. do you believe the claim that no more than 3 percent of this brand of golf bath exceed 1 62 oz in weight?

Explanation / Answer

Given

sample population = 24

weight of samples should not exceed 1.62 ounces

Claimed percentage of population exceeding 1.62 ounces is 3%

p=0.03

q= 1-p = 0.97

N=24

Doing Binomial distribution, results are

a)probability that none of the balls exceeds 1.62 ounces is

p(x=0)= 0.484

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b) probability that atleast one of the random samples exceeds 1.62 ounces is

p(x>0)=1-p(x=0)

1-0.4814

=0.5186

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c) p(x<=3)

p(x=0)+p(x=1)+p(x=2)+p(x=3)

=0.4814+0.3573+0.1271+0.0288

=0.9946

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d) p(x>=2)

1-p(x=0)+p(x=1)

=1-0.8387

=0.1613

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e) The claim for two balls selected is

p(x=2)=0.1217

given intially that claim is 3%

actual percentage is 12.17%

x P(X=x) 0 0.4814 1 0.3573 2 0.1271 3 0.0288 4 0.0047 5 0.0006

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