Question

The number of days (X) after mailout it takes a utility company to receive payment for a customer’s bill is a normal random variable with a mean of 31 days and a standard deviation of 6 days.The latest 2.5% of bills will be received more than how many days after mailout?

Answer 1

The latest 2.5% of bills will be received in 20 more days after mail-out.

Explanation:

We are given the following information in the question:

Mean, μ = 31 days

Standard Deviation, σ = 6 days

We are given that the distribution of The number of days (X) is a bell shaped distribution that is a normal distribution.

Formula:

`z_(score) = \displaystyle(x-\mu)/(\sigma)`

`P(X \leq x) = 0.025`

We have to find the value of x such that the probability is 0.025

`P(X \leq x) = 0.025`

`P( X \leq x) = P( z \leq \displaystyle(x - 31)/(6))=0.025`

Calculation the value from standard normal z table, we have,

`P( z \leq -1.960) = 0.025`

`\displaystyle(x - 31)/(6) = -1.960\\x = 19.24 \approx 20`

Hence, the latest 2.5% of bills will be received in 20 more days after mail-out.