Question

A drug tester claims that a drug cures a rare skin disease 84​% of the time. The claim is checked by testing the drug on 100 patients. If at least 80 patients are​ cured, the claim will be accepted. Find the probability that the claim will be rejected assuming that the​ manufacturer's claim is true. Use the normal distribution to approximate the binomial distribution if possible.. ROund to four decimal places

Answer 1

Solution:

Given that,

P = 0.84

1 - P = 0.16

n = 100

Here, BIN ( n , P ) that is , BIN (100 , 0.84)

According to normal approximation binomial,

X Normal

Mean = = n*P = 84

Standard deviation = =n*p*(1-p) = 13.44

We using continuity correction factor

P(X a ) = P(X > a - 0.5)

P(x > 79.5) = 1 - P(x < 79.5)

= 1 - P((x - ) / < (79.5 - 84) / 13.44)

= 1 - P(z < -1.23)

= 1 - 0.1093

= 0.8907

Probability = 0.8907