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The percentage of female Americans 25 years old and older who have completed 4 years of college or more is 26.1. In a random sample of 200 American women who are at least 25, what is the probability that at most 50 have completed 4 years of college or more?

0.3936

Intro Stats / AP Statistics

Chapter 6

The Normal Distribution

Section 4

The Normal Approximation to the Binomial Distribution

Probability Topics

Temple University

University of North Carolina at Chapel Hill

Cairn University

Idaho State University

Lectures

0:00

01:48

The Census Bureau's C…

04:54

People Who Have Some Colle…

04:13

Below are the percentages …

03:28

According to the National …

02:11

Graduate School Survey The…

00:57

The table shows the educat…

01:57

According to the U.S. Depa…

04:55

Percentage of People Who C…

09:35

ACT scores The composite s…

06:37

The levels of educationa…

04:28

Students on diets A sample…

02:51

Married Students Suppose t…

04:16

According to Federal Highw…

02:55

07:53

The age and gender demogra…

01:35

Conditional probability If…

02:01

Height The average height …

00:38

00:28

01:09

In $1975,$ approximately w…

Okay, Number 19 We have an equals 200 and we have P is 26.1% which converts 2.261 Our mean is just end times P. And you should get 52.2. Standard deviation is a square root of NP, which we said was 52.2 times Q, which is one minus p and that gives us 6.21 rounded to two decimals. All right, we want to find the probability that X is less than or equal to 50. And when you look at the conversion table continuity conversion table, you have X is less center equal to you. Add 0.5 and remove the equal sign. So I'm going to remove the equal sign and add 0.5 to 50. And that's gonna be our new X value. So Z equals X minus the mean divided by the standard deviation, and you should get a Z score of negative 0.27 Okay, When you look up that number on the Z score table, you should get point 3936 okay. And we're looking for X is less than 50.5. So that's exactly what we want. And if we just convert this, the percentage we get 39.36% and that's for number 19.

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