Question

In a certain population, \(15 \%\) of the people have Rh-negative blood. A blood bank serving this population receives 92 blood donors on a particular day. a. What is the probability that 10 or fewer are Rh-negative? b. What is the probability that 15 to 20 (inclusive) of the donors are Rh- negative? c. What is the probability that more than 80 of the donors are Rh-positive?

Short answer

Answer: To calculate the probabilities, use the binomial probability formula and sum the probabilities for each relevant value of k: 1. P(X ≤ 10) = Σ P(X = k) for k = 0 to 10 2. P(15 ≤ X ≤ 20) = Σ P(X = k) for k = 15 to 20 3. P(X ≤ 11) = Σ P(X = k) for k = 0 to 11 (Note: This is the same as having more than 80 Rh-positive donors)

Step-by-step solution

Calculate the probability that 10 or fewer are Rh-negative

We need to find the probability of having 0 to 10 Rh-negative donors. We will calculate the probabilities for each value of k (from 0 to 10) and sum them up: P(X ≤ 10) = Σ P(X = k) for k = 0 to 10

Calculate the probability for 15 to 20 (inclusive) of the donors are Rh-negative

We need to find the probability of having 15 to 20 Rh-negative donors. We will calculate the probabilities for each value of k (from 15 to 20) and sum them up: P(15 ≤ X ≤ 20) = Σ P(X = k) for k = 15 to 20

Calculate the probability that more than 80 of the donors are Rh-positive

We need to find the probability of having more than 80 Rh-positive donors, which means having fewer than 12 Rh-negative donors. We will calculate the probabilities for each value of k (from 0 to 11) and sum them up: P(X ≤ 11) = Σ P(X = k) for k = 0 to 11 Note that P(X ≤ 11) represents the probability of having 11 or fewer Rh-negative donors, which is the same as having more than 80 Rh-positive donors.