Question

question 4
the probability of a single customer purchasing an extended warranty is 0.35
if there are 7 customers, what is the probability that 5 will purchase an extended warranty?
use binomial formula. show all work.
four decimal places
edit format table
12pt paragraph b i u a

Explanation:

Step1: Identify the binomial formula parameters

The binomial formula is \(P(X = k)=C(n,k)\times p^{k}\times(1 - p)^{n - k}\), where \(n = 7\) (number of customers), \(k = 5\) (number of customers purchasing extended warranty), \(p=0.35\) (probability of a single customer purchasing), and \(1-p = 0.65\). The combination formula \(C(n,k)=\frac{n!}{k!(n - k)!}\), so \(C(7,5)=\frac{7!}{5!(7 - 5)!}=\frac{7!}{5!2!}=\frac{7\times6}{2\times1}=21\).

Step2: Calculate the probability

Substitute the values into the binomial formula: \(P(X = 5)=21\times(0.35)^{5}\times(0.65)^{2}\).
First, \((0.35)^{5}=0.35\times0.35\times0.35\times0.35\times0.35 = 0.0052521875\).
Second, \((0.65)^{2}=0.65\times0.65 = 0.4225\).
Then, \(21\times0.0052521875\times0.4225=21\times0.002219048=0.0466\).

Answer:

\(0.0466\)