David's gasoline station offers 4 cents off per gallon if the customer pays in cash. Past evidence indicates that 40% of all customers pay in cash. During a one-hour period, 15 customers buy gasoline at this station. What is the probability that more than 8 and less than 12 customers pay in cash?

The probability that more than 8 and less than 12 customers pay in cash is 0.0931.

Step-by-step explanation:

Let X = a customer at David's gasoline station pay in cash.

The probability of a customer paying in cash is, P (X) = p = 0.40

The number of customers at the gasoline station during a 1-hour period is,

n = 15.

Then the random variable X follows a binomial distribution, Bin (15, 0.40).

The probability function for a Binomial distribution is:

Compute the probability that more than 8 and less than 12 customers pay in cash as follows:

Thus, the probability that more than 8 and less than 12 customers pay in cash is 0.0931.

see attached

step-by-step explanation:

given the function as;

write the equation replacing f(x) with y

form   and fill a table containing values of y with corresponding values of x

you can take a range for   values of x as -3≤x≤3

solving for x=-3

for x=-2

repeat the same procedure to get the values of y for the remaining ,x=-1 to x=3

plot the values of y against values   of x and obtain the following graph