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The Practice of Statistics for AP

David Moore,Daren Starnes,Dan Yates

$Math Studyset Vaia Explanations$ Math

4th Edition · 809 pages

ISBN: 9781319113339

Chapter 2: Q 4.3. (page 103)

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

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 median could be shown as:

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Most popular questions from this chapter

Length of pregnancies The length of human pregnancies from conception to birth varies according to a distribution that is approximately Normal with mean of $266$ days and standard deviation of $16$ days. For each part, follow the four-step process.

(a) At what percentile is a pregnancy that lasts days (that’s about $8$ months)?

(b) What percent of pregnancies last between $240$ and $270$ days (roughly between $8$ months and $9$ months)?

(c) How long do the longest $20$ % of pregnancies last?

T2.3. Rainwater was collected in water collectors at $30$ different sites near an industrial complex, and the amount of acidity (pH level) was measured. The mean and standard deviation of the values are $4.60$ and $1.10$ , respectively. When the pH meter was recalibrated back at the laboratory, it was found to be in error. The error can be corrected by adding $0.1 pH$ units to all of the values and then multiplying the result by $1.2$ . The mean and standard deviation of the corrected pH measurements are

(a) $5.64, 1.44$

(b) $5.64, 1.32$

(c) $5.40, 1.44$

(d) $5.40, 1.32$

(e) $5.64, 1.20$

Use Table A to ﬁnd the value $z$ from the standard Normal distribution that satisﬁes each of the following conditions. In each case, sketch a standard Normal curve with your value of $z$ marked on the axis. Use your calculator or the Normal Curve applet to check your answers.

Working backward

(a) The $63$ rd percentile.

(b) $75$ % of all observations are greater than $z$ .

Use Table A in the back of the book to find the proportion of observations from a standard Normal distribution that fall in each of the following regions. In each case, sketch a standard Normal curve and shade the area representing the region.

$z < 1.39$

T2.11. As part of the President's Challenge, students can attempt to earn the Presidential Physical Fitness Award or the National Physical Fitness Award by meeting qualifying standards in five events: curl-ups, shuttle run, sit and reach, one-mile run, and pull-ups. The qualifying standards are based on the $1985$ School Population Fitness Survey. For the Presidential award, the standard for each event is the $85 t h$ percentile of the results for a specific age group and gender among students who participated in the $1985$ survey. For the National award, the standard is the $50 t h$ percentile. To win either award, a student must meet the qualifying standard for all five events.
Jane, who is $9$ years old, did $40$ curl-ups in one minute. Matt, who is $12$ years old, also did $40$ curl-ups in one minute. The qualifying standard for the Presidential award is $39$ curl-ups for Jane and $50$ curl-ups for Matt. For the National award, the standards are $30$ and $40$ , respectively.
(a) Compare Jane's and Matt's performances using percentiles. Explain in language simple enough for someone who knows little statistics to understand.
(b) Who has the higher standardized value ( $z$ -score), Jane or Matt? Justify your answer.

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