Question

find the probability of exactly 6 successes in 7 trials of a binomial experiment in which the probability of success is 80%.

p = ? %

round to the nearest tenth of a percent.

Explanation:

Step1: Recall the binomial probability formula

The binomial probability formula is \(P(X = k)=C(n,k)\times p^{k}\times(1 - p)^{n - k}\), where \(n\) is the number of trials, \(k\) is the number of successes, \(p\) is the probability of success, and \(C(n,k)=\frac{n!}{k!(n - k)!}\)

Step2: Identify the values of \(n\), \(k\), and \(p\)

Here, \(n = 7\), \(k = 6\), \(p=0.8\), and \(1-p = 0.2\)

Step3: Calculate the combination \(C(n,k)\)

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Step4: Substitute the values into the binomial probability formula

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Step5: Convert the decimal to a percentage

\(0.3670016\times100 = 36.70016\%\)

Answer:

\(36.7\%\)