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Chapter 4: Q88E (page 192)

A sample of \({\rm{15}}\) female collegiate golfers was selected and the clubhead velocity (km/hr) while swinging a driver was determined for each one, resulting in the following data

The corresponding \({\rm{z}}\) percentiles are

Short Answer

Expert verified

Yes

Step by step solution

01

Definition of Probability

Club head speed, as the name implies, refers to how quickly the club head moves when you strike your shot. At impact with the ball, the speed is measured, and it is virtually always done with the driver.

02

Resulting the data

Although there is some curvature in the probability plot, it is (perhaps) appropriate to employ estimating methods that assume a normal population distribution.

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Most popular questions from this chapter

The authors of the article "A Probabilistic Insulation Life Model for Combined Thermal-Electrical Stresses" (IEEE Trans. on Elect. Insulation, \({\rm{1985: 519 - 522}}\)) state that "the Weibull distribution is widely used in statistical problems relating to aging of solid insulating materials subjected to aging and stress." They propose the use of the distribution as a model for time (in hours) to failure of solid insulating specimens subjected to \({\rm{AC}}\) voltage. The values of the parameters depend on the voltage and temperature; suppose \({\rm{\alpha = 2}}{\rm{.5}}\) and \({\rm{\beta = 200}}\) (values suggested by data in the article).

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a. Show that if X has a normal distribution with parameters \({\rm{\mu }}\) and\({\rm{\sigma }}\), then \({\rm{Y = aX + b}}\) (a linear function of X ) also has a normal distribution. What are the parameters of the distribution of Y (i.e., E(Y) and V(Y)) ? (Hint: Write the cdf of\({\rm{Y,P(Y}} \le {\rm{y)}}\), as an integral involving the pdf of X, and then differentiate with respect to y to get the pdf of Y.)

b. If, when measured in\(^{\rm{^\circ }}{\rm{C}}\), temperature is normally distributed with mean 115 and standard deviation 2 , what can be said about the distribution of temperature measured in\(^{\rm{^\circ }}{\rm{F}}\)?

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