Question

g At a certain gas station, 30% of all customers use the restroom. What is the probability that, out of the next 10 customers, (a) exactly 4 will use the restroom

Answer 1

`P(x=4) = 0.200`

Explanation:

Given

`n=10` --- selected customers

`x = 4` --- those that are expected to use the restroom

`p =30\% = 0.30` --- proportion that uses the restroom

Required

`P(x = 4)`

The question illustrates binomial probability and the formula is:

`P(x) = ^nC_x * p^x * (1 - p)^(n - x)`

So, we have:

`P(x=4) = ^(10)C_4 * (0.30)^4 * (1 - 0.30)^(10 - 4)`

`P(x=4) = ^(10)C_4 * (0.30)^4 * (0.70)^6`

`P(x=4) = 210* (0.30)^4 * (0.70)^6`

`P(x=4) = 0.200`