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Chapter 2: Q R2.4. (page 147)

Density curves The following figure is a density curve that models a distribution of quantitative data. Trace the curve onto your paper.

a. What percent of observations have values less than 13? Justify your answer.

b. Mark the approximate location of the median. Explain your choice of location.

c. Mark the approximate location of the mean. Explain your choice of location.

Short Answer

Expert verified

Part (a) The 92percent of observations have values less than 13

Part (b) The mean's approximate location is 7

Part (c) The mean's approximate location is 10

Step by step solution

01

Part (a) Step 1: Given information

As per the given graph,

P (X > 13) = 0.08

02

Part (a) Step 2: Calculation

The fraction of observations with values less than 13 can be determined using the formula:

P(X<13)=1鈭�P(X鈮�13)=1鈭�0.08=0.92

Thus, the required answer is 0.92

03

Part (b) Step 1: Explanation

Because the graph is slanted to the right. It signifies that the mode is higher than the median, and the median is higher than the mean. The distribution ranges from 0to 20Consider that the median is less than ten times the mean, implying that the median is less than ten times the mean. As a result, the median's approximate location is 7

04

Part (c) Step 1: Explanation

Because the graph is slanted to the right. It signifies that the mode is higher than the median, and the median is higher than the mean. The distribution ranges from 0to 20As a result, the average is around ten.

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