The united states golf association usga tests new brands of...

The United States Golf Association (USGA) tests new brands of golf balls to assure that they meet USGA specifications. One test involves measuring the average distance traveled when the ball is hit by a machine called “Iron Byron’. Past tests have indicated that the population standard deviation of the distances “Iron Byron” hits golf balls is 10 meters. How many golf balls should be hit by “lron Byron” such that the 90% confidence interval for mean distance for the new brand is 2 meters wide?

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Transcript

00:01 Once again, welcome to a new problem.

00:03 This time we're dealing with confidence interval.

00:07 So we're looking at confidence interval.

00:09 And when you think about confidence interval for means, you have x bar plus minus margin of error.

00:18 The margin of error is z alpha over 2 sigma over radical n.

00:24 Assuming population standard deviation, assuming population standard deviation is known.

00:41 So if you know the population standard deviation, that's what's going to happen.

00:46 We're given a test for golf balls.

00:49 And in this test, we're looking at the average distances traveled when the balls are hit by the iron byron.

00:59 It just so happens that the standard deviation for the distances traveled is 10.

01:05 We want to determine n, which happens to be the number of golf balls hit given a 90 % confidence.

01:18 The error level is 2 meters.

01:21 So we want to find n.

01:23 We do know that because the population standard deviation is known, the error level, as you can recall, is z alpha over 2 sigma over radical n.

01:37 The reason why we're doing z alpha over 2 is because the confidence level is 1 minus alpha.

01:46 And so the tails have a probability of 1 half.

01:50 So the critical values on both sides is both negative and positive z alpha over 2.

01:57 We can multiply both sides by radical n...

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