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Chapter 2: Q 25. (page 108)

Density curves Sketch a density curve that might describe a distribution that is symmetric but has two peaks.

Short Answer

Expert verified

Density curve is

Step by step solution

01

Step 1. Given

Density curves is a distribution that is symmetric but has two peaks.

02

Step 2. Concept

A density curve is the graph of a continuous distribution.

03

Step 3. Explanation 

A symmetrical density curve with two peaks that looks like this:

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Most popular questions from this chapter

Comparing bone density Refer to the previous exercise. One of Judy鈥檚 friends, Mary, has the bone density in her hip measured using DEXA. Mary is 35 years old. Her bone density is also reported as 948g/cm2, but her standardized score isz=0.50. The mean bone density in the hip for the reference population of 35-year-old women is 944grams/cm2.

(a) Whose bones are healthier鈥擩udy鈥檚 or Mary鈥檚? Justify your answer.

(b) Calculate the standard deviation of the bone density in Mary鈥檚 reference population. How does

this compare with your answer to Exercise 13(b)? Are you surprised?

Teacher raises A school system employs teachers at salaries between \(28,000 and \)60,000. The teachers鈥� union and the school board are negotiating the form of next year鈥檚 increase in the salary schedule.

(a) If every teacher is given a flat \(1000 raise, what will this do to the mean salary? To the median salary? Explain your answers.

(b) What would a flat\)1000 raise do to the extremes and quartiles of the salary distribution? To the standard deviation of teachers鈥� salaries? Explain your answers.

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.

Weights aren鈥檛 Normal The heights of people of the same gender and similar ages follow Normal distributions reasonably closely. Weights, on the other hand, are not Normally distributed. The weights of women aged 20 to 29 have mean 141.7 pounds and median 133.2 pounds. The first and third quartiles are 118.3 pounds and 157.3 pounds. What can you say about the shape of the weight distribution? Why?

Questions T2.9 and T2.10 refer to the following setting. Until the scale was changed in 1995, SAT scores were based on a scale set many years ago. For Math scores, the mean under the old scale in the 1990swas 470and the standard deviation was 110. In 2009, the mean was 515and the standard deviation was 116 .
T2.10. Jane took the SAT in 1994and scored 500. Her sister Colleen took the SAT in 2009and scored 530. Who did better on the exam, and how can you tell?
(a) Colleen-she scored 30 points higher than Jane.
(b) Colleen-her standardized score is higher than Jane's.
(c) Jane-her standardized score is higher than Colleen's.
(d) Jane-the standard deviation was bigger in 2009.
(e) The two sisters did equally well-their z-scores are the same.
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