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Chapter 2: Q 29. (page 108)

Biking accidents What is the mean 渭 of the density curve pictured in Exercise 27? (That is, where would the curve balance?) What is the median? (That is, where is the point with an area 0.5 on either side?)

Short Answer

Expert verified

The mean and median are equal to 1.5

Step by step solution

01

Step 1. Given

The points with an area of0.5are on either side.

02

Step 2. Concept

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

03

Step 3. Calculation

The rectangle's balancing point is the distribution's mean point. As a result, the mean is calculated as follows: 渭=3+0/2=1.5

The median of the asymmetric 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=1.5

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

Therefore, both the mean and median are equal to 1.5

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Most popular questions from this chapter

T2.3. Rainwater was collected in water collectors at 30different sites near an industrial complex, and the amount of acidity (pH level) was measured. The mean and standard deviation of the values are 4.60and 1.10, respectively. When the pH meter was recalibrated back at the laboratory, it was found to be in error. The error can be corrected by adding 0.1pHunits to all of the values and then multiplying the result by 1.2. The mean and standard deviation of the corrected pH measurements are

(a)5.64,1.44

(b)5.64,1.32

(c)5.40,1.44

(d)5.40,1.32

(e)5.64,1.20

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.

R2.6 Horse pregnancies Bigger animals tend to carry their young longer before birth. The length of horse pregnancies from conception to birth varies according to a roughly Normal

distribution with a mean of 336 days and a standard deviation of 3 days. Use the 68-95-99.7 rule to answer the following questions.

(a) Almost all (99.7%)horse pregnancies fall in what range of lengths?

(b) What percent of horse pregnancies are longer than 339 days? Show your work.

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�2.05and 0.78

(b) zis between 鈭�1.11and 鈭�0.32

Comparing batting averages Three landmarks of baseball achievement are Ty Cobb鈥檚 batting average of 420in 1911, Ted Williams鈥檚 406in 1941, and George Brett鈥檚 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.
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