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Chapter 2: Q 30. (page 108)

A uniform distribution What is the mean μ of the density curve pictured in Exercise 28? What is the median?

Short Answer

Expert verified

The mean and median are equal to 0.5

Step by step solution

01

Step 1. Given

Over the range of 0 to 1, The curve maintains the same value 1 and is 0 outside the range of values. This signifies that the data described by this distribution has a uniformly distributed range of values between 0and 1

02

Step 2. Concept

The p% percentile of a distribution is the value having p% of the observations less than it.

03

Step 3. Calculation 

The rectangle's balancing point is the distribution's mean point. As a result, the mean is calculated as follows:

μ=1+0/2=0.5

The median of a symmetric distribution is the point where the area of the curve is equal on both sides. As a result, the median is calculated as follows:

Md=arealiestotheleft=arealiestotherightMd=0.5

The uniform distribution's mean and median are presented below.

Therefore both the mean and median are equal to 0.5

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Most popular questions from this chapter

SAT versus ACT Eleanor scores 680 on the SAT Mathematics test. The distribution of SAT scores is

symmetric and single-peaked, with mean 500and standard deviation 100. Gerald takes the American College Testing (ACT) Mathematics test and scores 27. ACT scores also follow a symmetric, singlepeaked distribution—but with mean 18 and standard deviation 6. Find the standardized scores for both students. Assuming that both tests measure the same kind of ability, who has the higher score?

About what percent of the cockroaches have weights between 76 and 84 grams?

(a) 99.7%

(b) 95%

(c) 68%

(d) 47.5%

(e) 34%

Baseball salaries Brad Lidge played a crucial role as the Phillies’ “closer,” pitching the end of many games throughout the season. Lidge’s salary for the 2008 season was $6,350,000

(a) Find the percentile corresponding to Lidge’s salary. Explain what this value means.

(b) Find the z-score corresponding to Lidge’s salary. Explain what this value means.

Blood pressure Larry came home very excited after a visit to his doctor. He announced proudly to his wife, “My doctor says my blood pressure is at the 90thpercentile among men like me. That means I’m better off than about 90% of similar men.” How should his wife, who is a statistician, respond to Larry’s statement?

Normal is only approximate: ACT scores Scores on the ACT test for the 2007 high school graduating class had mean 21.2and standard deviation 5.0. In all, 1,300,599students in this class took the test. Of these, 149,164had scores higher than 27and another 50,310had scores exactly 27. ACT scores are always whole numbers. The exactly Normal N(21.2,5.0)distribution can include any value, not just whole numbers. What’s more, there is no area exactly above 27under the smooth Normal curve. So ACT scores can be only approximately Normal. To illustrate this fact, find

(a) the percent of 2007ACT scores greater than 27.

(b) the percent of 2007ACT scores greater than or equal to 27.

(c) the percent of observations from theN(21.2,5.0) distribution that are greater than 27. (The percent greater than or equal to 27 is the same, because there is no area exactly over 27.)
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