Question

According to the National Endowment for the Arts, 20% of U.S. women attended a musical play in 2002. Use this information to answer questions 6 & 7:

a.) In a random sample of 15 U.S. women, what is the probability that fewer than 7 attended a musical play in 2002.

b.) Calculate the mean and variance of the number of U.S. women who attended a musical play in 2002 for a sample of size 25.

Answer 1

a)

Let X be a random variable representing the number of U.S. women who attended the musical play in 2002.

Then X is Binomial random variable with sample size n=15, probability of success p= 0.2 as 20% of U.S. women attended the musical play in 2002.

So,

Here

=0.9819

b)

We know that for binomial distribution mean is and variance is

here n=25 p=0.2

so mean =np= variance =

you can find more about binomial distribution in any statistics book (probability distribution).

Thank you!

answered by: anonymous