Question

The state department of transportation is coordinating road crews to fix potholes after a particularly snowy winter. Initial estimates gave an average of 7.8 potholes per mile of highway. Find the probability that there are 11 or more potholes in a randomly selected one-mile stretch of highway. Use Excel to find the probability.

Answer 1

P(X≥11) = 0.1648

Explanation:

Given

Mean, μ = 7.3

Potholes, n = 11

The interpretation of the question is to calculate P(X ≥ 11)

It is known that

P(X) = P(1) + P(2) +.......+P(infinite)

We can say that

P(X) = P(X≤10) + P(X>10)

Make P(X>10) the subject of formula

P(X>10) = P(X) - P(X≤10)

P(X>10) is equivalent to P(X≥11) and P(X) = 1.

By substituton, we have

P(X≥11) = 1 - P(X≤10)

So, we'll solve P(X≤10) using the following steps using n as 10.

To solve the above question using Microsoft Office Excel, follow the highlighted steps below

1. First goto FORMULAS tan

2. Select INSERT FUNCTION.

3. Select the POISSON.DIST function.

4. Enter the values for the number of events and the mean of occurrences per interval. In this case, enter 10 and 7.8, in that order and 1 for Cumulative since this is a cumulative probability.

5. Press OK.

Excel would display the probability.

In this case, it is 0.83523

Remember that

P(X≥11) = 1 - P(X≤10)

By substituton

P(X≥11) = 1 - 0.83523

P(X≥11) = 0.16477

Approximately,

P(X≥11) = 0.1648

(See attachment)