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Chapter 2: Q. 2.4 (page 119)

Use Table A to find the value zfrom the standard Normal distribution that satisfies each of the following conditions. In each case, sketch a standard Normal curve with your value of zmarked on the axis.

4. The 20thpercentile

Short Answer

Expert verified

The value of zis -0.84. And the standard Normal curve is,

Step by step solution

01

Given Information 

Given that,20th percentile

Value of z=?

02

Explanation 

Using standard normal table,

P(Z<z)=20%P(Z<z)=0.20P(Z<-0.84)=0.20z=-0.84

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Most popular questions from this chapter

T2.2. For the Normal distribution shown, the standard deviation is closest to

(a) 0

(b) 1

(c) 2

(d) 4

(e) 5

Use Table A in the back of the book to find the proportion of observations from a standard Normal distribution that fall in each of the following regions. In each case, sketch a standard Normal curve and shade the area representing the region.

3.−0.56<z<1.81

Speed limits According to the Los Angeles Times, speed limits on California highways are set at the 85th percentile of vehicle speeds on those stretches of road. Explain what that means to someone who knows little statistics.

Comparing batting averages Three landmarks of baseball achievement are Ty Cobb’s batting average of 420in 1911, Ted Williams’s 406in 1941, and George Brett’s 390in 1980. These batting averages cannot be compared directly because the distribution of major league batting averages has changed over the years. The distributions are quite symmetric, except for outliers such as Cobb, Williams, and Brett. While the mean batting average has been held roughly constant

by rule changes and the balance between hitting and pitching, the standard deviation has dropped over time. Here are the facts: Compute the standardized batting averages for Cobb, Williams, and Brett to compare how far each stood above his peers.

R2.8 Working backward

(a) Find the number zat the 80th percentile of a standard Normal distribution.

(b) Find the number localid="1649404103275" zsuch that localid="1649404108890" 35%of all observations from a standard Normal distribution are greater than localid="1649404115271" z.

- Use Table A to find the percentile of a value from any Normal distribution and the value that corresponds to a given percentile.
See all solutions

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