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Chapter 2: Q. 1.2 (page 114)

The distribution of heights of young women aged 18to 24is approximately N(64.5,2.5)

2. What percent of young women have heights greater than 67inches? Show your work.

Short Answer

Expert verified

The percentage of young women have heights greater than 67inches are 5.6923%.

Step by step solution

01

Given information

Heights of young women aged between=18to24.

Percentage of young women heights greater than 67inches=?

02

Explanation 

Normal distribution =N(64.5,2.5)

Here mean value μ=64.5

Variance σ2=2.5

Thenσ=1.58114

Then z-score, z=x-μσ

Here need to find the percentage of heights greater than 67,

localid="1649920459043" P(x>67)=Pz>67−64.52.5P(x>67)=p(z>1.58114)

From the table of normal distribution,

p(x>67)=0.056923

Convert into percentage,

localid="1649920477292" =0.056923×100%p(x>67)=5.6923%

The normal distribution curve is,

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Most popular questions from this chapter

Each year, about 1.5million college-bound high school juniors take the PSAT. In a recent year, the mean score on the Critical Reading test was 46.9and the standard deviation was10.9. Nationally, 5.2%of test takers earned a score of 65 or higher on the Critical Reading test’s 20to 80scale.9

PSAT scores Scott was one of 50junior boys to take the PSAT at his school. He scored 64on the Critical Reading test. This placed Scott at the 68th percentile within the group of boys. Looking at all 50boys’ Critical Reading scores, the mean was 58.2and the standard deviation was 9.4

(a) Write a sentence or two comparing Scott’s percentile among the national group of test-takers and among the 50boys at his school.

(b) Calculate and compare Scott’s z-score among these same two groups of test-takers.

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. Use your calculator or the Normal Curve applet to check your answers.

Working backward

(a) The 63rd percentile.

(b) 75% of all observations are greater than z.

Follow the method shown in the examples to answer each of the following questions. Use your calculator or the Normal Curve applet to check your answers.

2. People with cholesterol levels between 200and 240mg/dlare at considerable risk for heart disease. What percent of 14-year-old boys have blood cholesterol between 200and 240mg/dl?

Shoes How many pairs of shoes do students have? Do girls have more shoes than boys? Here are data from a random sample of 20 female and 20 male students at a large high school:

(a) Find and interpret the percentile in the female distribution for the girl with 22pairs of shoes.

(b) Find and interpret the percentile in the male distribution for the boy with 22 pairs of shoes.

(c) Who is more unusual: the girl with22 pairs of shoes or the boy with 22 pairs of shoes? Explain.

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

(a) 0

(b) 1

(c) 2

(d) 4

(e) 5
See all solutions

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