Question

Who is the king of late night tv an internet survey estimates that, when given a choice between david letterman and jay leno, 57% 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. Find the probability distribution for y, the number of viewers in the sample who prefer leno.

Answer 1

The probability distribution for the number of viewers in the sample who prefer Jay Leno is as follows: P(Y = 0) = 0.0791, P(Y = 1) = 0.2683, P(Y = 2) = 0.3059, and P(Y = 3) = 0.3477.

Step-by-step explanation:

To find the probability distribution for the number of viewers in the sample who prefer Jay Leno, we can use the binomial distribution. In this case, the probability of success (viewers prefer Jay Leno) is 0.57, and the number of trials is 3.

To calculate the probability distribution, we need to calculate the probabilities for each possible outcome: 0, 1, 2, and 3 viewers prefer Jay Leno.

The probability of 0 viewers preferring Jay Leno is (0.43)³ = 0.0791.

The probability of 1 viewer preferring Jay Leno is (0.43)²(0.57) = 0.2683.

The probability of 2 viewers preferring Jay Leno is (0.43)(0.57)² = 0.3059.

The probability of 3 viewers preferring Jay Leno is (0.57)³ = 0.3477.

Therefore, the probability distribution is as follows:

P(Y = 0) = 0.0791

P(Y = 1) = 0.2683

P(Y = 2) = 0.3059

P(Y = 3) = 0.3477