Question

5 multiple choice 1.43 points according to a recent survey, 68% of adult americans consumed alcohol before turning 21 years old. in a random sample of 50 adult americans, find the probability that exactly 35 consumed alcohol before turning 21 years old. 0.2474 0.1168 0.3522 0.1936

Explanation:

Step1: Identify 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 in a single trial, and \(C(n,k)=\frac{n!}{k!(n - k)!}\)

Step2: Assign values to the formula

Here, \(n = 50\), \(k = 35\), \(p=0.68\), and \(1-p = 0.32\)

First, calculate the combination \(C(50,35)=\frac{50!}{35!(50 - 35)!}=\frac{50!}{35!15!}\)

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Then, \(p^{k}=(0.68)^{35}\) and \((1 - p)^{n - k}=(0.32)^{15}\)

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Using a binomial probability calculator or software (since calculating the factorials and exponents by hand is very time - consuming), we find that \(P(X = 35)\approx0.1168\)

Answer:

B. 0.1168