Question

A group of 14 students' cholesterol levels are tested. suppose the probability of a student having a healthy cholesterol level is 0.30. (a) a binomial experiment has a fixed number of trials, n. for this experiment, what is the value of n? (b) what is the probability of a success? (c) what is the probability that exactly four out of 14 students have healthy cholesterol levels? (round your answer to three decimal places.)

Answer 1

a. The value of n for this binomial experiment is 14. b. The probability of a success is 0.30. c. The probability that exactly four out of 14 students have healthy cholesterol levels can be calculated using the binomial probability formula.

Step-by-step explanation:

a. The fixed number of trials, n, is equal to the number of students in the group. In this case, n = 14 since there are 14 students.

b. The probability of a success, p, is given as 0.30, which is the probability of a student having a healthy cholesterol level.

c. To find the probability that exactly four out of 14 students have healthy cholesterol levels, we can use the binomial probability formula:

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

Plugging in the values, we have:

P(X = 4) = (14 choose 4) * 0.30^4 * (1-0.30)^(14-4)

Calculating this expression will give the desired probability.