/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 96 Mrs. Diaz has two children: a 3-... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 96

Mrs. Diaz has two children: a 3-yearold boy 43 inches tall and a 10 -year-old girl 57 inches tall. Threeyear-old boys have a mean height of 38 inches and a standard deviation of 2 inches, and 10 -year-old girls have a mean height of \(54.5\) inches and a standard deviation of \(2.5\) inches. Assume the distributions of boys' and girls' heights are unimodal and symmetric. Which of Mrs. Diaz's children is more unusually tall for his or her age and gender? Explain, showing any calculations you perform. (Source: www.kidsgrowth.com)

Short Answer

Expert verified
The Z-score for Mrs. Diaz鈥檚 son is 2.5 and the Z-score for Mrs. Diaz鈥檚 daughter is 1. The son's Z-score is higher than the daughter's, indicating that he is more unusually tall for his age and gender than his sister.

Step by step solution

01

Compute the Z-Score for Mrs. Diaz鈥檚 son

The z-score formula, \(Z = \frac{x - 碌}{蟽}\), is used where: \(x\) is the raw score, \(碌\) is the population mean, and \(蟽\) is the standard deviation. Substituting the given values (43 inches is the son's height, 38 inches is the mean height, and 2 inches is the standard deviation), we get \(Z_{son} = \frac{43 - 38}{2}.\)
02

Compute the Z-Score for Mrs. Diaz鈥檚 daughter

The same formula as above is applied: \(Z = \frac{x - 碌}{蟽}\) where \(x\) is the raw score, \(碌\) is the population mean, and \(蟽\) is the standard deviation. The given values are substituted (57 inches is the daughter's height, 54.5 inches is the mean height, and 2.5 inches is the standard deviation), resulting in \(Z_{daughter} = \frac{57 - 54.5}{2.5}.\)
03

Compare the Z-Scores

The Z-scores of Mrs Diaz's son and daughter are compared. The child with the higher Z-score is considered more unusually tall for their age and gender.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In the most recent summer Olympics, do you think the standard deviation of the running times for all men who ran the 100 -meter race would be larger or smaller than the standard deviation of the running times for the men's marathon? Explain.

State College Tuition The tuition costs (in dollars) for a sample of four-year state colleges in California and Texas are shown below. Compare the means and the standard deviations of the data and compare the state tuition costs of the two states in a sentence or two. (Source: calstate.edu, texastribune.com) \(\mathrm{CA}: 7040,6423,6313,6802,7048,7460\) \(\mathrm{TX}: 7155,7504,7328,8230,7344,5760\)

The table show the gold medal Olympic times (in seconds) for the 200-meter run. Data are shown for the first five Olympics of the 1900 s and five more recent Olympics in the 2000s. (Source: World Almanac and Book of Facts 2017) $$ \begin{array}{|c|c|c|c|} \hline \text { Olympic Year } & \text { Time } & \text { Olympic Year } & \text { Time } \\ \hline 1900 & 22.2 & 2000 & 20.1 \\ \hline 1904 & 21.6 & 2004 & 19.8 \\ \hline 1908 & 22.6 & 2008 & 19.3 \\ \hline 1912 & 21.7 & 2012 & 19.3 \\ \hline 1920 & 22.0 & 2016 & 19.8 \\ \hline \end{array} $$ a. Find and interpret (report in context) the mean and standard deviation of the winning times for the first five Olympics of the 1900 s. Round to the nearest hundredth of a second. b. Find the mean and standard deviation of the winning times for the more recent Olympics. c. Compare the winning times of the early \(1900 \mathrm{~s}\) and the \(2000 \mathrm{~s}\) Olympics. Are recent winners faster or slower than those of the early 1900 s? Which group has less variation in its winning times?

The prices (in \$ thousand) of a sample of three-bedroom homes for sale in South Carolina and Tennessee are shown in the following table. Write a report that compares the prices of these homes. In your report, answer the questions of which state had the most expensive homes and which had the most variability in home prices. (Source: Zillow.com) $$ \begin{array}{|c|c|} \hline \text { South Carolina } & \text { Tennessee } \\ \hline 292 & 200 \\ \hline 323 & 205 \\ \hline 130 & 400 \\ \hline 190 & 138 \\ \hline 110 & 190 \\ \hline 183 & 292 \\ \hline 185 & 127 \\ \hline \end{array} $$ $$ \begin{array}{|c|c|} \hline \text { South Carolina } & \text { Tennessee } \\ \hline 160 & 183 \\ \hline 205 & 215 \\ \hline 165 & 280 \\ \hline 334 & 200 \\ \hline 160 & 220 \\ \hline 180 & 125 \\ \hline 134 & 160 \\ \hline 221 & 302 \\ \hline \end{array} $$

Assume that men's heights have a distribution that is symmetric and unimodal, with a mean of 69 inches and a standard deviation of 3 inches. a. What men's height corresponds to a \(z\) -score of \(2.00\) ? b. What men's height corresponds to a z-score of \(-1.50 ?\)
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.