/*! 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} Q. 6.48 Refer to the simulation of human... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Q. 6.48 (page 263)

Refer to the simulation of human gestation periods discussed in Example \(6.4\) on page \(259\).

a. Sketch the normal curve for human gestation periods

b. Simulate \(1000\) human gestation periods.

c. Approximately what values would you expect for the sample mean and sample deviation of the \(1000\) observations? Explain your answers.

d. Obtain the sample mean and sample standard deviation of the \(1000\) observations, and compare your answers to your estimates in part (c).

e. Roughly what would you expect a histogram of the \(1000\) observation to look like? Explain your answer.

f. Obtain a histogram of the \(1000\) observations, and compare your result to your expectation in part (e).

Short Answer

Expert verified

Part a.

Part b.

Part c. The expected population鈥檚 mean will be \(266\) and standard \(16\).

Part d. The population鈥檚 mean will be \(\bar{x}=266.62\) and standard \(s=15.8152\)

Part e.

Step by step solution

01

Part a. Step 1. Given information

The mean and standard are given

\(\mu =266\)

\(\sigma =16\)

02

Part a. Step 2. Calculation

Randomly generate \(x=1000\) numbers from the normal distribution with mean \(\mu=266\) and standard deviation \(\sigma=16\).

Then Using MATLAB draw a graph.

Program:

clc

clear

closeall

\(x=norminv(rand(1000,1),266,16);\)

hist(x)

\(set(gca,'linewidth',1.2,'fontsize',12)\)

axis square

Query:

  • First, we have defined the \(1000\) random numbers whose mean and standard deviation is \(266\) and \(16\).
  • Then using function 鈥渉ist鈥� draw a figure.
03

Part b. Step 1. Calculation

Randomly generate \(x=1000\) numbers from the normal distribution with mean \(\mu=266\) and standard deviation \(\sigma=16\).

Then Using MATLAB generate the matrix of \(1000\) numbers.

Program:

clc

clear

closeall

\(x=norminv(rand(1000),266,16)\);

Query:

  • First, we have defined the \(1000\) random numbers whose mean and standard deviation is \(266\) and \(16\).
  • Then using function 鈥渉ist鈥� draw a figure.
04

Part c. Step 1. Given information

The number of observations is given

\(x=500\)

05

Part c. Step 2. Calculation

Calculate the mean:

\(\bar{x}=\frac{\sum_{i-1}^{n}x_{i}}{n}=\frac{\sum_{i-1}^{1000}x_{i}}{1000}\)

The expected mean will be

\(\bar{x}=266\)

Calculate the expected standard deviation

\(s=\sqrt{\frac{\sum_{i-1}^{n}(x_{i}-\bar{x})^{2} }{n-1}}=\sqrt{\frac{\sum_{i-1}^{1000}(x_{i}-\bar{x})^{2} }{999}}\)

After calculating we will get

\(s=16\)

The population mean will be \(266\) and standard \(16\).

06

Part d. Step 1. Calculation

Calculate the mean:

\(\bar{x}=\frac{\sum_{i-1}^{n}x_{i}}{n}=\frac{\sum_{i-1}^{1000}x_{i}}{1000}\)

The expected mean will be

\(\bar{x}=266.62\)

Calculate the expected standard deviation

\(s=\sqrt{\frac{\sum_{i-1}^{n}(x_{i}-\bar{x})^{2}}{n-1}}=\sqrt{\frac{\sum_{i-1}^{1000}(x_{i}-\bar{x})^{2} }{999}}\)

After calculating we will get

\(s=15.8152\)

The population鈥檚 mean will be \(\bar{x}=266.62\) and standard \(s=15.8152\).

07

Part e. Calculation

Randomly generate \(x=1000\) numbers from the normal distribution with mean \(\mu=266\) and standard deviation \(\sigma=16\).

Then Using MATLAB draw a graph.

Program:

clc

clear

closeall

\(x=norminv(rand(1000,1),266,16);\)

hist(x)

\(set(gca,'linewidth',1.2,'fontsize',12)\)

axis square

Query:

  • First, we have defined the \(1000\) random numbers whose mean and standard deviation is \(266\) and \(16\).
  • Then using function 鈥渉ist鈥� draw a figure.

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

20. Sketch the normal curve having the parameters

a. 渭=-1and蟽=2

b. 渭=3and蟽=2

c. 渭=-1and蟽=0.5

Students in an introductory statistics course at the U.S. Air Force Academy participated in Nabisco's "Chips Ahoy! 1.000 Chips Challenge" by confirming that there were at least 1000 chips in every18-ounce bag of cookies that they examined. As part of their assignment, they concluded that the number of chips per bag is approximately normally distributed. Could the number of chips per bag be exactly normally distributed? Explain your answer. [SOURCE: B. Warner and J. Rutledge, "Checking the Chips Ahoy! Guarantee," Chance, Vol. 12(1). pp. 10-14]

Obtain the z-score that has an area 0.80to its left under the standard normal curve.

Desert Samaritan Hospital in Mesa, Arizona, keeps records of emergency room traffic. Those records reveal that the times between arriving patients have a special type of reverse-J-shaped distribution called an exponential distribution. The records also show that the mean time between arriving patients is 8.78 minutes.

a. Use the technology of your choice to simulate four random samples of75 interarrival times each.

b. Obtain a normal probability plot of each sample in part (a).

c. Are the normal probability plots in part (b) what you expected? Explain your answer.

Under what circumstances is using a normal probability plot to assess the normality of a variable usually better than using a histogram, stem-and-leaf diagram, or dotplot?
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

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.