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Chapter 8: Q 8.112. (page 342)

Batting Averages. An issue of Scientific American revealed that batting averages, xof major-league baseball players are normally

distributed and have a mean of 0.270 and a standard deviation of 0.031 For samples of 20 batting averages, identify the distribution of each variable.

a. x¯-0.2700.031/20

b. x¯-0.270s/20

Short Answer

Expert verified

Part (a) Follows the conventional normal distribution, which has a mean of 0and a standard deviation of 1

Part (b) With(n-1) degrees of freedom, it follows the t-distribution.

Step by step solution

01

Part (a) Step 1: Given information

Batting average, xof major - league baseball players are normally distributed and have a mean μ=0.270and S.D σ=0.031

Sample size n=20

02

Part (a) Step 2: Concept

The formula used: z=x¯-μσn

03

Part (a) Step 3: Calculation

x¯-μσn=x¯-0.2700.03120Follows standard normal distribution i.e. normal distribution with mean 0 and S.D 1

04

Part (b) Step 1: Calculation

x¯-μssn=x¯-0.2700.03120 Follows t-distribution with (n-1) degrees of freedom.

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