Question

Who is the king of the late night TV? An internet survey estimates that, when given a choice between David Letterman and Jay Leno, 52% of the population prefers to watch Jay Leno. Suppose that you randomly select three late night TV watchers and ask them which of the two talk show hosts they prefer.

a-Find the probability distribution for x, the number of people in the sample of three who would prefer Jay Leno.
b-What is the probability that exactly one of the three would prefer Jay Leno?
c-What are the population mean and standard deviation for the random variable x?

Answer 1

Use a normal approximation to the binomial distribution.

Your values are the following:
p = .52, q = 1 - p = .48, x = 1, and n = 3

Find mean and standard deviation.
mean = np = (3)(.52) = ?
sd = √npq = √(3)(.52)(.48) = ?

I'll let you finish the calculations.

Once you have the mean and standard deviation, use z-scores and z-table to find probability.

P(0.5 < x < 1.5) =
P[(0.5 - mean)/sd] < z < [(1.5 - mean)/sd]

Once you have the two z-scores (substitute the mean and sd calculated), find the difference between the two using a z-table. This will be your probability.

I hope this will help get you started.