STATISTICS
posted by Hayli on .
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.
aFind the probability distribution for x, the number of people in the sample of three who would prefer Jay Leno.
bWhat is the probability that exactly one of the three would prefer Jay Leno?
cWhat are the population mean and standard deviation for the random variable x?

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 zscores and ztable to find probability.
P(0.5 < x < 1.5) =
P[(0.5  mean)/sd] < z < [(1.5  mean)/sd]
Once you have the two zscores (substitute the mean and sd calculated), find the difference between the two using a ztable. This will be your probability.
I hope this will help get you started.