Question

Approximately 15% of Americans have a blood type of B. The local blood bank has 80 donors stop by on a given day (which can be considered a random sample from the population). What is the probability that between 15% and 20% of the donors on a given day have a blood type of B?

Answer 1

Answer: the probability that between 15% and 20% of the donors on a given day have a blood type of B is 0.3944

Explanation:

Given that;

Binomial Distribution

n = 80

p = 0.15

q = 1 - p = 0.85

Mean = μ = np = 80 X 0.15 = 12

SD = σ = √(npq) = √(80 x 0.15 x 0.85) = -3.1937

Now; Assumptions in normal distribution to binomial distribution

- The sample size = n = 80 > 30 . Large sample

- np = 80 × 0.15 = 12 > 10

- nq = 80 × 0.85 = 68 > 10

so

80 × 0.15 = 12

80 × 0.20 = 16

To find P(12 < X < 16):

Z = (16 - 12) / 3.1937

= 4 / 3.1937

= 1.2525

Table of Area Under Standard Normal Curve gives area = 0.3944

Therefore the probability that between 15% and 20% of the donors on a given day have a blood type of B is 0.3944