Answered: The United States Golf Association…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter8: Applications Of Trigonometry

Section8.2: The Law Of Cosines

Problem 3E

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The United States Golf Association (USGA) tests all new brands of golf balls to assure that they meet USGA specifications. One of the tests is intended to measure the average distance traveled when the ball is hit by a machine called “Iron Byron”, a name inspired by the swing of the famous golfer Byron Nelson. The USGA proceeded to test with the Iron Byron machine over 250 golf balls of a new type called Ballistic, recording the distance travelled of each one. They then calculated a sample mean and the following 90% confidence interval [335.1; 337.1] (in meters). Based on USGA’s confidence interval they can conclude: HINT: Remember that we build confidence intervals around sample means - not individual observations.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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