A company tests all new brands of golf balls to ensure that they meet certain specifications. One test conducted is intended to measure the average distance traveled when the ball is hit by a machine. Suppose the company wishes to estimate the mean distance for a new brand to within 1.9 yards with 90 % confidence. Assume that past tests have indicated that the standard deviation of the distances the machine hits golf balls is approximately 14 yards. How many golf balls should be hit by the machine to achieve the desired accuracy in estimating the mean?

Question

Lailah Gaines

Mathematics

7 November, 03:07

A company tests all new brands of golf balls to ensure that they meet certain specifications. One test conducted is intended to measure the average distance traveled when the ball is hit by a machine. Suppose the company wishes to estimate the mean distance for a new brand to within 1.9 yards with 90 % confidence. Assume that past tests have indicated that the standard deviation of the distances the machine hits golf balls is approximately 14 yards. How many golf balls should be hit by the machine to achieve the desired accuracy in estimating the mean?

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Miriam Walker · Answer 1

385 golf balls

Step-by-step explanation:

margin of error = (z*) (s) / sqrt n

where z * = 1.96 with 5% / 2 = 0.025 area in each tail

margin of error = (z*) (s) / sqrt n

1.2 yards = (1.96) (12 yards) / sqrt n

solve for n

n = 384.16

385 golf balls (always round up)