Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

Women comprise 80.3% of all elementary school teachers. In a random sample of 300 elementary teachers, what is the probability that less than three-fourths are women?

0.0087

Intro Stats / AP Statistics

Chapter 6

The Normal Distribution

Section 4

The Normal Approximation to the Binomial Distribution

Probability Topics

Temple University

Missouri State University

University of North Carolina at Chapel Hill

Idaho State University

Lectures

0:00

Okay, Number 21 We have n equals 300. We have p equals 80.3% which is 0.803 All right, the mean is just n times P. And you should get to 40.9. And for the standard deviation, the square root of end times, P times Q, which is just one minus p. And you should get 6.89 rounded to two decimal places. Now they want to know the probability of less than 3/4. Okay, so we have to take the sample, which was 300 multiply that by 3/4. Okay, And that's gonna equal 225. So we want to find the probability that X is less than 225. Okay, when we goto our continuity conversion table, when X is less than a number, you subtract 0.5. Okay, so 2 25 minus 0.5 is to 24.5. That's gonna be our new X value. Now for Z, you do X minus the mean divided by the standard deviation, and you should get a Z score of negative 2.38 Okay. And When you look up that number on the Z score table, you should get 0.0 087 Okay, that's the probability that X is less than 2 24.5 That's exactly what we want. So just converting this to decimal moving over to places and you should get point 87% so that's number 21.

View More Answers From This Book

Find Another Textbook

00:59

Selecting Students How many ways can you pick 4 students from 10 students (6…

01:03

What formula is used to gain information about an individual data value when…

Cell Phone Models A particular cell phone company offers 4 models of phones,…

01:36

Why do most of the sample means differ somewhat from the population mean? Wh…

10:07

The average overseas trip cost is $\$ 2708$ per visitor. If we assume a norm…

04:18

Socks in a Drawer A drawer contains 11 identical red socks and 8 identical b…

01:57

Endangered Amphibians There are 9 endangered amphibian species in the United…

05:33

Rolling the Dice If three dice are rolled, find the probability of getting a…

07:41

The average teacher's salary in Connecticut (ranked first among states)…

09:12

In a study of the life expectancy of 500 people in a certain geographic regi…