/*! 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 101 Babies in the United States have... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 101

Babies in the United States have a mean birth length of \(20.5\) inches with a standard deviation of \(0.90\) inch. The shape of the distribution of birth lengths is approximately Normal. a. How long is a baby born at the 20 th percentile? b. How long is a baby born at the 50 th percentile? c. How does your answer to part b compare to the mean birth length? Why should you have expected this?

Short Answer

Expert verified
The length of a baby born at the 20th percentile is approximately 19.24 inches. The length of a baby born at the 50th percentile is 20.5 inches, which equals to the mean birth length. This outcome is expected as in a normal distribution, the mean, median (50th percentile) and mode are all equal.

Step by step solution

01

Calculate the length at the 20th percentile

To calculate the length at the 20th percentile, we need to use the standard normal distribution table or the Z-table. The 20th percentile corresponds approximately to a Z-score of -0.84. So the formula for calculating the length at the 20th percentile \(L_{20}\) would be \(L_{20}= \text{mean} + Z_{20} * \text{std_dev}\) where mean is 20.5, \(Z_{20}\) is -0.84, and std_dev is 0.9.
02

Calculate the length at the 50th percentile.

The same method applies to calculate the length at the 50th percentile. However, take note that the 50th percentile (median) corresponds to a Z-score of 0. Thus, the formula for calculating the length at the 50th percentile \(L_{50}\) would be \(L_{50} = \text{mean} + Z_{50}* \text{std_dev}\) where mean is 20.5, \(Z_{50}\) is 0, and std_dev is 0.9.
03

Comparing the calculated 50th percentile to the mean birth length.

Evaluate the results from step 2 and compare \(L_{50}\) with the given mean (20.5 inches). Also, justify the result theoretically.

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

The use of drones, aircraft without onboard human pilots, is becoming more prevalent in the United States. According to a 2017 Pew Research Center report, \(59 \%\) of American had seen a drone in action. Suppose 50 Americans are randomly selected. a. What is the probability that at least 25 had seen a drone? b. What is the probability that more than 30 had seen a drone? c. What is the probability that between 30 and 35 had seen a drone? d. What is the probability that more than 30 had not seen a drone?

Rule with z-Scores The Empirical Rule applies rough approximations to probabilities for any unimodal, symmetric distribution. But for the Normal distribution we can be more precise. Use the figure and the fact that the Normal curve is symmetric to answer the questions. Do not use a Normal table or technology. According to the Empirical Rule, a. Roughly what percentage of \(z\) -scores are between \(-2\) and 2 ? i. almost all iii. \(68 \%\) ii. \(95 \%\) iv. \(50 \%\) b. Roughly what percentage of \(z\) -scores are between \(-3\) and 3 ? i. almost all iii. \(68 \%\) ii. \(95 \%\) iv. \(50 \%\) c. Roughly what percentage of \(z\) -scores are between \(-1\) and 1 . i. almost all iii. \(68 \%\) ii. \(95 \%\) iv. \(50 \%\) d. Roughly what percentage of \(z\) -scores are greater than \(0 ?\) i. almost all iii. \(68 \%\) ii. \(95 \%\) iv. \(50 \%\) e. Roughly what percentage of \(z\) -scores are between 1 and \(2 ?\) i. almost all iii. \(50 \%\) ii. \(13.5 \%\) iv. \(2 \%\)

Colorado has a high school graduation rate of \(75 \%\). a. In a random sample of 15 Colorado high school students, what is the probability that exactly 9 will graduate? b. In a random sample of 15 Colorado high school students, what is the probability that 8 or fewer will graduate? c. What is the probability that at least 9 high school students in our sample of 15 will graduate?

When a certain type of thumbtack is flipped, the probability of its landing tip up (U) is \(0.60\) and the probability of its landing tip down (D) is \(0.40\). Now suppose we flip two such thumbtacks: one red, one blue. Make a list of all the possible arrangements using \(\mathrm{U}\) for up and \(\mathrm{D}\) for down, listing the red one first; include both UD and DU. Find the probabilities of each possible outcome, and record the result in table form. Be sure the total of all the probabilities is \(1 .\)

The distribution of red blood cell counts is different for men and women. For both, the distribution is approximately Normal. For men, the middle \(95 \%\) range from \(4.5\) to \(5.7\) million cells per microliter and for women, the middle \(95 \%\) have red blood cells counts between \(3.9\) and \(5.0\) million cells per microliter. a. What is the mean and the standard deviation of red blood cell counts for men? Explain your reasoning. b. What is the mean and the standard deviation of red blood cell counts for women? Explain your reasoning. c. Which gender shows more variation in red blood cell counts? Support your answer with appropriate statistics.
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

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.