Answer :
Answer:
The probability that of 15 trucks, less than 4 trucks have blowouts is 0.4613.
Step-by-step explanation:
Let X = number of trucks having a blowout during the test run.
The probability of a truck having a blowout during the test run is, p = 0.25.
The sample of trucks selected is of size, n = 15.
The random variable X follows a Binomial distribution with parameters n = 15 and p = 0.25.
The probability mass function of X is:
[tex]P(X=x)={15\choose x}0.25^{x}(1-0.25)^{15-x};\ x=0,1,2,3...[/tex]
Compute the probability that less than 4 trucks have blowouts as follows:
P (X < 4) = P (X = 0) + P (X = 1) + P (X = 2) + P (X = 3)
[tex]={15\choose 0}0.25^{0}(1-0.25)^{15-0}+{15\choose 1}0.25^{1}(1-0.25)^{15-1}\\+{15\choose 2}0.25^{2}(1-0.25)^{15-2}+{15\choose 3}0.25^{3}(1-0.25)^{15-3}\\=0.0134+0.0668+0.1559+0.2252\\=0.4613[/tex]
Thus, the probability that of 15 trucks, less than 4 trucks have blowouts is 0.4613.