A drug tester claims that a drug cures a rare skin disease 82% of the time. The claim is checked by testing the drug on 100 patients. If at least 74 patients are cured, the claim willI 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.)
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Given Information :
A drug tester claim that a drug cures a rare skin disease 82% of the time . The claim is checked by testing the drug on 100 patients . If at least 74 patients are cured , the claim will be accepted .
Sample size : n = 100
Probability of success : p = 82% = 0.82
The claim will be accepted when at least 74 patients are cured and thus the claim will be rejected when less than 74 patients are cured .
P (x < 74)
Requirements for normal distribution for the binomial distribution :
np > 5 and nq > 5
np = 100 (0.82) = 82 > 5
nq = n (1-p) = 100(1-0.82) =18 > 5
Thus the requirements are satisfied and thus it is appropriate to use the normal distribution .
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