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Chapter 2: Q.46 (page 131)

A Normal curve Estimate the mean and standard deviation of the Normal density curve in the figure below:

Short Answer

Expert verified

From the graph, we can calculate the mean is 10and the standard deviation is 2

Step by step solution

01

Given Information

A normal density curve is given in the question.

02

Explanation

It observed that the inflection points are 8and 12from the given graph.

So, μ+σ=12.

A peak value of 10is also shown in the graph, this represents the mean.μ=10.

We can determine the standard deviation by using the below equation.

μ+σ=12⇒10+σ=12⇒σ=2

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Most popular questions from this chapter

Use Table A to find the value zfrom the standard Normal distribution that satisfies 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.

Each year, about 1.5million college-bound high school juniors take the PSAT. In a recent year, the mean score on the Critical Reading test was 46.9and the standard deviation was 10.9Nationally, 5.2% of test-takers earned a score of 65 or higher on the Critical Reading test’s 20 to 80 scale. 9

PSAT scores How well did the boys at Scott’s school perform on the PSAT? Give appropriate evidence to support your answer.

Mrs. Munson is concerned about how her daughter’s 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.

Trace the density curve onto your paper. Mark the approximate location of the median.

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.
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