Question

Suppose that a technology task force is being formed to study technology awareness among instructors. Assume that ten people will be randomly chosen to be on the committee from a group of 28 volunteers, 20 who are technically proficient and eight who are not. We are interested in the number on the committee who are; technically proficient.; X; X

a. Between 4 and 6 people who are technically proficient.

b. Between 7 and 9 people who are technically proficient.

c. Exactly 10 people who are technically proficient.

d. More than 10 people who are technically proficient.

Answer 1

The random variable X represents the number of people who are technically proficient on the committee. The probability that there are between 4 and 6 people who are technically proficient is 0.787, or 78.7%.

Step-by-step explanation:

The random variable X represents the number of people on the committee who are technically proficient. In this case, X can take on values between 0 and 10, inclusive. This is because out of the 28 volunteers, 20 are technically proficient and 8 are not. Since the committee will consist of 10 people, the number of technically proficient people on the committee can range from 0 to 10.

To find the probability that X is between 4 and 6 people who are technically proficient, we need to calculate the probability of having 4, 5, or 6 people who are technically proficient on the committee. This can be done using the hypergeometric distribution formula:

P(X=k) = (C(20,k) * C(8,10-k)) / C(28,10)

For k = 4, P(X=4) = (C(20,4) * C(8,6)) / C(28,10) = 0.240

For k = 5, P(X=5) = (C(20,5) * C(8,5)) / C(28,10) = 0.319

For k = 6, P(X=6) = (C(20,6) * C(8,4)) / C(28,10) = 0.228

The probability that X is between 4 and 6 people who are technically proficient is the sum of these probabilities: 0.240 + 0.319 + 0.228 = 0.787, or 78.7%.