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Chapter 2: Q 4.1. (page 103)

Explain why this is a legitimate density curve.

Short Answer

Expert verified

Since, the curve is above the horizontal axis and the total area under the curve is 1, we have a legitimate density curve.

Step by step solution

01

Step 1. Given

02

Step 2. Concept

A curve is based on a density curve.

03

Step 3. Explanation

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. As a result, we obtain a valid density curve.

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Most popular questions from this chapter

The distribution of weights of 9-ounce bags of a particular brand of potato chips is approximately Normal with mean 渭=9.12ounces and standard deviation蟽=0.05ounces. Draw an accurate sketch of the distribution of potato chip bag weights. Be sure to label the mean, as well as the points one, two, and three standard deviations away from the mean on the horizontal axis.

Density curves Sketch a density curve that might describe a distribution that has a single peak and is skewed to the left.

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 10th percentile.

(b) 34% of all observations are greater thanz.

Measure up Clarence measures the diameter of each tennis ball in a bag with a standard ruler. Unfortunately, he uses the ruler incorrectly so that each of his

measurements is 0.2inches too large. Clarence鈥檚 data had a mean of 3.2inches and a standard deviation of 0.1 inches. Find the mean and standard deviation of the corrected measurements in centimeters (recall that 1 inch = 2.54 cm).

Shoes How many pairs of shoes do students have? Do girls have more shoes than boys? Here are data from a random sample of 20 female and 20 male students at a large high school:

(a) Find and interpret the percentile in the female distribution for the girl with 22pairs of shoes.

(b) Find and interpret the percentile in the male distribution for the boy with 22 pairs of shoes.

(c) Who is more unusual: the girl with22 pairs of shoes or the boy with 22 pairs of shoes? Explain.
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