Respuesta :
Answer:
The probability that exactly 2 buyers would prefer red car is 0.0317.
Step-by-step explanation:
Let the random variable X represent the number of buyers would prefer red car.
The probability of the random variable X is, p = 0.40.
A random sample of n = 14 buyers are selected.
The event of a buyer preferring a red car is independent of the other buyers.
The random variable X thus follows a Binomial distribution with parameters n = 14 and p = 0.40.
The probability mass function of X is:
[tex]P(X=x)={14\choose x}(0.40)^{x}(1-0.40)^{14-x};\ x=0,1,2,3...[/tex]
Compute the probability that exactly 2 buyers would prefer red car as follows:
[tex]P(X=2)={14\choose 2}(0.40)^{2}(1-0.40)^{14-2}[/tex]
[tex]=91\times 0.16\times 0.0021768\\=0.031694208\\\approx 0.0317[/tex]
Thus, the probability that exactly 2 buyers would prefer red car is 0.0317.
