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Chapter 2: Q 4.4. (page 103)

Now mark the approximate location of the mean. Explain why the mean and median have the relationship that they do in this case.

Short Answer

Expert verified

The curve is

Step by step solution

01

 Step 1. Given

The figure is:

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. Explanation

In the figure, the approximate location of the mean and median could be shown as:

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Most popular questions from this chapter

Old folks Here is a stem plot of the percent of residents aged 65 and older in the50states:

(a) Find and interpret the percentile for Colorado, which has 10.1%of its residents aged 65or older.

(b) Find and interpret the percentile for Rhode Island, with 13.9%of residents aged 65or older.

(c) Which of these two states is more unusual? Explain.

Brent is a member of the school鈥檚 basketball team. The mean height of the players on the team is 76 inches. Brent鈥檚 height translates to a z-score of 鈭�0.85 in the team鈥檚 height distribution. What is the standard deviation of the team members鈥� heights?

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.

Shopping spree The figure below is a cumulative relative frequency graph of the amount spent by

50 consecutive grocery shoppers at a store.

(a) Estimate the interquartile range of this distribution. Show your method.

(b) What is the percentile for the shopper who spent $19.50?

(c) Challenge: Draw the histogram that corresponds to this graph.

Mrs. Munson is concerned about how her daughter鈥檚 height and weight compared with those of other girls of the same age. She uses an online calculator to determine that her daughter is at the 87th percentile for weight and the 67th percentile for height. Explain to Mrs. Munson what this means.

Questions 3 and 4 relate to the following setting. The graph displays the cumulative relative frequency of the lengths of phone calls made from the mathematics department office at Gabaldon High last month.
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