Probability of testing samples

Question

For 4 and 5, use the following information: According to the Florida Department of Health, the positive rate for coronavirus tests on Wednesday was 7.75%. Suppose 435 people in Gainesville receive coronavirus tests. Round your answers to 3 decimal places.

1.      What is the probability that exactly 32 people will test positive for coronavirus?

2.      What is the probability that less than 30 people will test positive for coronavirus?

Answer 1

For the first

435 C 32 x 0.0775^32 x (1-0.0775) ^ 403

For the second

Approximate the binomial distribution with a normal here

n = 435

p = 0.0775

q = 1-p = 0.9225

B(n,p) is approximately N(np, √npq)

So N (33.7125, 5.5767)

So you need p (X<30).

On a TI-84

2nd vars

normalcdf

lower -1e99

upper 30

mean 33.7125

sd 5.5767

answer 0.253

(You can also calculate p (X=0) + ... P(X=29) to get an exact answer where

p (X=n) = 435 C n x 0.0775^n x 0.9225^(435-n)