Question

97​% of Dr.​ William's patients end up with​ 20-30 vision or better. Find the probability that exactly 5 of her next 8 patients end up with​ 20-30 vision or better.

Answer 1

p = probability of a patient being 20-30 vision or better.

p = 0.97

Let X be number of patients that are 20-30 vision or better from next 8 patients.

X ~ Binomial distribution with n = 8 and p = 0.97

To find P(X = 5)

We use Excel function BINOM.DIST to find the probability.

P(X = 5) = BINOM.DIST(5, 8, 0.97, FALSE)

= 0.0013

P(exactly 5 of her next 8 patients end up with​ 20-30 vision or better.) = 0.0013