The number of viewers of American Idol has a mean

protisvitfc

protisvitfc

Answered question

2021-12-01

The number of viewers of American Idol has a mean of 29 million with a standard deviation of 5 million. Assume this distribution follows a normal distribution. What is the probability that next week’s show will:
Have between 30 and 34 million viewers?

Answer & Explanation

juniorekze

juniorekze

Beginner2021-12-02Added 18 answers

The average number of American Idol viewers is μ=29 million and the standard deviation is σ=5 million. 
Let x represent the audience size.
X is between 30 and 34 
P(30<X<34)=P(30μ<Xμ<34μ) 
=P(30μσ<Xμσ<34μσ) 
=P(30295<z<34295) 
=P(14<z<55) 
=P(0.25<z<1) 
Calculate because the two points are on the same side of the mean.
P(0<z<0.25), P(0<z<1) and subtract the two probabilities. 
P(30<X<34)=P(0<z<1)-P(0<z<0.25) 
=0.3413-0.0987 (from Appendix B1.) 
=0.2426

Do you have a similar question?

Recalculate according to your conditions!

New Questions in College Statistics

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?