Refer a friend and earn $50 when they subscribe to an annual planRefer Now

Get the answer to your homework problem.

Try Numerade Free for 30 Days

Like

Report

Normal Probability The mean height of American men between 20 and 29 years old is 69 inches, and the standard deviation is 3 inches. A 20- to 29-year-old man is chosen at random from the population. The probability that he is 6 feet tall or taller is$$P(72 \leq x<\infty)=\int_{72}^{\infty} \frac{1}{3 \sqrt{2 \pi}} e^{-(x--\omega)^{2} / 18} d x$$$$\begin{array}{l}{\text { (a) Use a graphing utility to graph the integrand. Use the }} \\ {\text { graphing utility to convince yourself that the area between }} \\ {\text { the } x \text { -axis and the integrand is } 1 \text { . }}\end{array}$$$$\begin{array}{l}{\text { (b) Use a graphing utility to approximate } P(72 \leq x<\infty) \text { . }} \\ {\text { (c) Approximate } 0.5-P(69 \leq x \leq 72) \text { using a graphing }} \\ {\text { utility. Use the graph in part (a) to explain why this result }} \\ {\text { is the same as the answer in part (b). }}\end{array}$$

NO ANSWER AVAILABLE

Calculus 2 / BC

Chapter 8

Integration Techniques and Improper Integrals

Section 8

Improper Integrals

Integration Techniques

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

Boston College

Lectures

01:11

In mathematics, integratio…

06:55

In grammar, determiners ar…

01:07

Men's heights A repor…

07:41

According to the National …

01:37

It is believed that the me…

00:54

Use the pdf in example 7.2…

00:53

00:57

05:04

Overweight Men For a rando…

10:09

The heights of U.S. men ar…

01:21

Find the mean and standard…

this question has a lot to do with graphing utilities on because there is at least 100 different graphing you to tease out there. I'm not gonna answer that far. It just depends too much on the specific. Your sense you used to give a one coherent answer. Um, but there's one part of the question that I can give an answer to, and then is the sort of the second bar questions. See? So let's graph the function they're talking about. Um, if this is, uh, 69 this is 72 that say this is than 66. The function looks something like this. No, my drawings are, of course, absolutely terrible. And the actual function looks difference that the height will change the profile of these like different. But this captures the most important parts. Especially one of the most important properties of dysfunction is that it's symmetric around 69. So the left half of this guy and it right off of this guy are same. Now, the question asks us to explain why the probability that someone is Toller? Uh then, uh, 72 is the same s 1/2 minus the probability that someone is between 69 and 72. And this is a question we can't answer based on this graph. Because what are these? Uh, what are these things in terms of the graph? So the probability that you're taller than 72. That's cool that the red area is this area area photograph to the right of 72. Now, what is the program? Is it that you're between 69 72 inches? That is this green area right here. Now, because this graph is symmetric, the total area of this site, um, equals the area on this side because it's perfectly symmetric around 69. This is one of the more important properties off the normal distribution, which this question is about. That means that that and since it's a probability distribution like the total integral off, his entire function is one. And since the two halfs are equal, the moat must be half, which means that green plus red equals 1/2. And that explains why, uh, the formula given into question, uh, works out because it's 1/2 of the area under a probability function which has total integral well

View More Answers From This Book

Find Another Textbook

In mathematics, integration is one of the two main operations in calculus, w…

In grammar, determiners are a class of words that are used in front of nouns…

Men's heights A report of the National Center for Health Statistics say…

According to the National Health Survey, the heights of adult males in the U…

It is believed that the mean height of high school students who play basketb…

Use the pdf in example 7.2 to find the probability that a randomly selected …

Overweight Men For a random sample of 60 over-weight men, the mean of th…

The heights of U.S. men are normally distributed with a mean of 69 inches an…

Find the mean and standard deviation for the binomial random variable $x$ wi…

00:39

Rearrangement of Series Does rearranging theterms of a convergent series…

01:14

Determining Absolute and Conditional Convergence In Exercises 41-58, determi…

CONCEPT CHECKAlternating Series An alternating series doesnot meet t…

05:41

$$\begin{array}{l}{\text { Comparing Integrals }} \\ {\text { (a) Show t…

Using the Limit Comparison Test In Exercises $17-26,$ use the Limit Comparis…

00:37

Matching In Exercises $9-14,$ match the series with the graph of its sequenc…

01:30

If $0 < a_{n}$ $\leq b_{n}$ and $\sum_{n=1}^{\infty} b_{n}$ diverges,the…

00:52

Determining Convergence or Divergence In Exercises $37-40$ , use the polynom…

00:56

Using the Root Test In Exercises $39-52,$ use the Root Test to determine the…

01:24

Using a Series You delete a finite number of terms from a divergent series. …

92% of Numerade students report better grades.

Try Numerade Free for 30 Days. You can cancel at any time.

Annual

0.00/mo 0.00/mo

Billed annually at 0.00/yr after free trial

Monthly

0.00/mo

Billed monthly at 0.00/mo after free trial

Earn better grades with our study tools:

Textbooks

Video lessons matched directly to the problems in your textbooks.

Ask a Question

Can't find a question? Ask our 30,000+ educators for help.

Courses

Watch full-length courses, covering key principles and concepts.

AI Tutor

Receive weekly guidance from the world’s first A.I. Tutor, Ace.

30 day free trial, then pay 0.00/month

30 day free trial, then pay 0.00/year

You can cancel anytime

OR PAY WITH

Your subscription has started!

The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

Receive weekly guidance from the world's first A.I. Tutor, Ace.

Mount Everest weighs an estimated 357 trillion pounds

Snapshot a problem with the Numerade app, and we'll give you the video solution.

A cheetah can run up to 76 miles per hour, and can go from 0 to 60 miles per hour in less than three seconds.

Back in a jiffy? You'd better be fast! A "jiffy" is an actual length of time, equal to about 1/100th of a second.