The average hourly charge of plumbers in the Denver area is $84.00 with a standard deviation of $4.00. Assume that the hourly charges of the plumbers in Denver are normally distributed. If a person living in Denver calls a random plumber, what is the probability that the plumber will charge at least $86.00 per hour. Express your answer as a decimal between 0 and 1, to the nearest hundredth.

The probability is 0.31

Step-by-step explanation:

In this question, we are tasked with calculating the probability that a random plumber called at Denver will charge an amount greater than $86 given the mean and the standard deviation.

Firstly, we calculate the standard score of $86 using the mean and the standard deviation.

Mathematically;

z-score = (x-mean) / SD

where x = 86, mean = 84 and SD = 4

z-score = (86-84) / 4 = 2/4 = 0.5

Hence, we want to calculate P (z ≥ 0.5)

Using standard table

P ((z ≥ 0.5) = 1 - P (z ≤ 0.5) = 1 - (0.19146 + 0.5) = 0.30854

To the nearest hundredth = 0.31