Question

A drug tester claims that a drug cures a rare skin disease 81% of the time. The claim is checked by testing the drug on 100 patients. If at least 78 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.

The probability is_______

(Round to four decimal places as needed.)

Answer #1

Solution:

We are given n=100, p=0.81, q=1 p = 1 – 0.81 = 0.19

We have to find P(X<78)

We have to use normal approximation to binomial distribution.

Mean = np = 100*0.81 = 81

SD = sqrt(npq) = sqrt(100*0.81*0.19) = 3.923009

Z = (X – mean) / SD

Z = (78 - 81) / 3.923009

Z = -0.76472

P(Z<-0.76472) = P(X<78) = 0.222219

(by using z-table or excel)

**Required probability =**
**0.2222**

(Without using continuity correction factor)

By using continuity correction factor 0.5, we have to find P(X<78) = P(X<77.5)

Z = (77.5 - 81) / 3.923009

Z = -0.89217

P(Z<-0.89217) = P(X<77.5) = 0.18615

(by using z-table or excel)

**Required probability = 0.1862**

(Using continuity correction factor)

A drug tester claims that a drug cures a rare skin disease 68%
of the time. The claim is checked by testing the drug on 100
patients. If at least 60 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.

A drug tester claims that a drug cures a rare skin disease 66%
of the time. The claim is checked by testing the drug on 100
patients. If at least 61 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.

A drug tester claims that a drug cures a rare skin disease 72%
of the time. The claim is checked by testing the drug on 100
patients. If at least 65 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.

A drug tester claims that a drug cures a rare skin disease 83%
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 manufacturers claim is true. *round four
decimals

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