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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 1.5 yards with 95​%
confidence. Assume that past tests have indicated that the standard deviation of the distances the machine hits golf balls is approximately 15 yards. How many golf balls should be hit by the machine to achieve the desired accuracy in estimating the​ mean?