Question

The wait time for a computer specialist on the phone is on average 45.7 minutes with standard deviation 7.6 minutes. What is the probability that the wait time for help would be 50 minutes or more? Draw and label a picture of a normal distribution with both x and z number lines underneath as in class examples, marked with all relevant values. Show all calculations and state areas to 4 decimal places.

Below what number of minutes would the 4% of shortest wait times occur?

Answer 1

The following is obtained graphically:

Part 2

We know that X is normally distributed, with parameters:

μ=45.7, σ=7.6

We need to find a score x so that the corresponding cumulative normal probability is equal to 0.04. Mathematically, x is such that:

Pr(X≤x)=0.04

The corresponding z score so that the cumulative standard normal probability distribution is 0.04 is

zc​=-1.7507

This value of zc​=-1.7507 can be found either with Excel, or with a normal distribution table. Hence, the X score associated with the 0.04 cumulative probability is

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