Question

A sign on the pumps at a gas station encourages customers to have their oil checked, and claims that one out of 8 cars needs to have oil added. If this is true, what is the probability of each of the following:

a) Exactly three out of the next eight cars needs oil. Probability =
b) At least three out of the next eight cars needs oil. Probability =
c) At most 6 out of the next 8 cars needs oil. Probability =

Answer 1

0.0561,0.0673,0.999997

Explanation:

Given that a sign on the pumps at a gas station encourages customers to have their oil checked, and claims that one out of 8 cars needs to have oil added.

X- no of cars that need oil in a sample of 8 cars is binomial with p = 1/8

since each car is independent of the other and there are only two outcomes.

a) Exactly three out of the next eight cars needs oil.

Probability =
`P(X=3) =0.0561`

b) At least three out of the next eight cars needs oil.

Probability =
`P(X\geq 3)\\= 0.0673`

c) At most 6 out of the next 8 cars needs oil.

Probability =
`P(X\leq 6)\\=0.999997`