Answer to Question #338666 in Statistics and Probability for sadiya

Question #338666

On an average 5% of the population in an area suffers from Diabetes. What is the probability that out of 7 persons chosen at random from this area with less than and equals to three suffer from the disease


1
Expert's answer
2022-05-09T16:19:14-0400

Let X=X= the number of persons suffer from the disease :XBin(n,p).X\sim Bin(n, p).

Given n=7p=0.05,q=1p=0.95.n=7 p=0.05, q=1-p=0.95.


P(X)=P(X=0)+P(X=1)P(X\le)=P(X=0)+P(X=1)

+P(X=2)+P(X=3)+P(X=2)+P(X=3)

=(70)(0.05)0(0.95)70+(71)(0.05)1(0.95)71=\dbinom{7}{0}(0.05)^{0}(0.95)^{7-0}+\dbinom{7}{1}(0.05)^{1}(0.95)^{7-1}

0.0002927\approx0.0002927

+(72)(0.05)2(0.95)72+(73)(0.05)3(0.95)73+\dbinom{7}{2}(0.05)^{2}(0.95)^{7-2}+\dbinom{7}{3}(0.05)^{3}(0.95)^{7-3}

=0.99980642188=0.99980642188


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