Who is the king of late night TV An Internet survey estimates that, when given a choice

Problem 3.19

Who is the king of 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. Three late night TV watchers are randomly selected and asked which of the two-talk show hosts they prefer. a Find the probability distribution for Y, the number of viewers in the sample who prefer Leno. b Construct a probability histogram for p(y). c What is the probability that exactly one of the three viewers prefers Leno? d What are the mean and standard deviation for Y? e What is the probability that the number of viewers favoring Leno falls within 2 standard deviations of the mean?

                                                             Step by step solution

Step 1 of 5

Given:

The percentage of the population who prefers to watch Jay Leno is p = 0.52.

Let Y be a random variable representing the number of viewers in the sample who prefer Leno.

a. In the given scenario, the random variable Y can take the values as 0, 1, 2 and 3.

The random variable Y will follow the binomial distribution.

Mathematically,

The probability mass function of the binomial distribution is given as:

For y = 0, the probability is given as:

For y = 1, the probability is given as:

For y = 2, the probability is given as:

For y = 3, the probability is given as:

The probability distribution formed is: