Question

It is believed that approximately 75 youth now have insurance due to the health care law. Suppose this is true, and let X equal the number of American youth in a random sample of n = 15 with private health insurance.

a) How is X distributed?

b) Find the probability that X is at least 10.

c) Find the probability that X is at most 10.

d) Find the probability that X is equal to 10.

e) Give the mean, variance and standard deviation of X

Answer 1

X is the number of American youth in a random sample of n = 15 with private health insurance

a. X follows a Binomial Distribution with n=15 and the probability of success p= 0.75

b.

Where

So

= 0.8516

c.

= [1-0.8516] + 0.1651 = 0.3135

d.

e. Mean = n*p = 15*0.75 = 11.25

Variance = n*p*(1-p) = 15*0.75*0.25 = 2.8125

Standard deviation =