Statistics and Probability Answers

1. If a student randomly guesses at five multiple-choice questions, find the probability that the student gets exactly three correct. Each question has five possible choices.

Left-tailed test, variance unknown, 𝛼 = 0.01, n = 23

A population consists of the five numbers 2, 3, 6, 8, and 11.

Consider the samples of size 2 that can be drawn from this

population.

A. List all the possible samples and the corresponding mean.

B. Construct the sampling distribution of the sample mean.

Suppose that the racial/ethnic distribution in a large city is given by the table that follows.

Black Hispanic Other

20% 15% 65%

Suppose that a jury of twelve members is chosen from this city in such a way that each resident has an equal probability of being selected independently of every other resident.

Lets find probability that the jury contains:

a. three Black, two Hispanic, and seven other members.

b. four Black and eight other members.

c. at most one Black member.

Two chess players have the probability Player A would win is 0.40, Player B would win is 0.35, game would end in a draw is 0.25. If these two chess players played 12 games, what is the probability that Player A would win 7 games, Player B would win 2 games, the remaining 3 games would be drawn?

The probabilities of a machine manufacturing 0,1,2,3 and 5 defective parts in one day are 0.75,0.17,0.04,0.025,0.01 and 0.005 respectively.Find the mean of the probability distribution.

80% of all business startups in the IT industry report that they generate a profit in their first year. If a sample of 10 new IT business startups is selected, find the probability that exactly seven will generate a profit in their first year.

Two chess players have the probability Player A would win is 0.40, Player B would win is 0.35,

game would end in a draw is 0.25. If these two chess players played 12 games, what is the probability that Player A would win 7 games, Player B would win 2 games, the remaining 3 games would be drawn?

In a restaurant an average of two out of every five customers asks for water with their meal. A family

of ten members arrives in the restaurant. What is the probability that:

a. Exactly seven members ask for water?

b. Less than nine members ask for water?

Suppose a researcher goes to a small college of 200 faculty, 12 of which have blood type O-negative. She obtains a simple random sample of the faculty. Let the random variable X represent the number of faculty in the sample of size that have blood type O-negative.

a. What is the probability that 3 of the faculty have blood type O-negative?

b. What is the probability that at least one of the faculty has blood type O-negative?