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Chapter 2: Q 4.2. (page 103)

About what proportion of observations lie between 7and 8?

Short Answer

Expert verified

The proportion of observation lies between 7 and 8 is 0.12

Step by step solution

01

Step 1. Given

02

Step 2. Concept

A density curve has the same area underneath it as the horizontal axis and is always on or above it. A density curve depicts the overall pattern of distribution. The proportion of all observations that fall within an interval of values on the horizontal axis is represented by the area under the curve and above that interval.

03

Step 3. Calculation

Calculate the percentage of observations that fall between 7 and 8.

That is correct.

P(7<X<8)

P(7<X<8)=鈭�78f(x)dx=鈭�780.12dx=0.12

As a result, 100% of the observations are lie between 7 and 8 is 0.12

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Most popular questions from this chapter

Use Table A to 铿乶d the proportion of observations from the standard Normal distribution that satis铿乪s each of the following statements. In each case, sketch a standard Normal curve and shade the area under the curve that is the answer to the question. Use your calculator or the Normal Curve applet to check your answers.

More Table A practice

(a) zis between 鈭�1.33and 1.65

(b) zis between 0.50and1.79

Use Table A to 铿乶d the value zfrom the standard Normal distribution that satis铿乪s 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.

T2.6. The figure shown is the density curve of a distribution. Five of the seven points marked on the density curve make up the five-number summary for this distribution. Which two points are not part of the five-number summary?

(a) Band E
(b) C and F
(c) C and E
(d) B and F
(e) A and G.

T2.1. Many professional schools require applicants to take a standardized test. Suppose that 1000 students take such a test. Several weeks after the test, Pete receives his score report: he got a 63, which placed him at the 73rd percentile. This means that

(a) Pete's score was below the median.

(b) Pete did worse than about 63%of the test takers.

(c) Pete did worse than about 73%of the test takers.

(d) Pete did better than about 63%of the test takers.

(e) Pete did better than about 73%of the test takers.

R2.10 Grading managers Many companies "grade on a bell curve" to compare the performance of their managers and professional workers. This forces the use of some low-performance ratings, so that not all workers are listed as "above average." Ford Motor Company's "performance management process" for a time assigned 10%A grades, 80%B grades, and 10%C grades to the company's 18,000managers. Suppose that Ford's performance scores really are Normally distributed. This year, managers with scores less than 25received C's, and those with scores above 475received A's. What are the mean and standard deviation of the scores? Show your work.
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