Question

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.

Answer #1

Claim will be accepted if P[ X >= 65 ]

Claim will be rejected if P[ X < 65 ].

The population proportion of success is p = 0.72, and the sample size is n= 100. We need to compute P[ X < 65 ].

The population mean is computed as:

and the population standard deviation is computed as:

Therefore, we get that

so then, we conclude that P[ X < 65 ]. ≈ 0.0739, which ends the calculation of the requested probability

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 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.)

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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