I’m Laticia Bourne, and I’ll be giving a step by step explanation on how to solve problem #7 on Exam #3’s review sheet, which reads:

The quarterly profits for a large company are normally distributed with  million and million.  What is the probability that the profits for the next quarter will lie between $100 million and $150 million?

Step 1.

The first thing that’s always best to do is pull out the information given.

Mean: 134 million

Standard Deviation: 20 million

In this case, we have two x’s

X = 150

X= 100

Step 2.

Before we can find the probability, we first have to find two z-scores for our two x’s. We do this by using the following equation:

z = x – mean/standard deviation

We’ve already pulled out the information needed for that equation in Step 1, so now to plug those numbers in for each of our x’s:

1. z = 150-134/20

z= 16/20

z = 0.8

2. z = 100-134/20

z= -34/20

z = -1.7

Step 3.

Now that we have our two z-scores, we then use the z-table to look up the area for each one. You should find that the area for the z-score 0.8 is .7881 and the area for the z-score -1.7 is .0446.

Step 4.

The final step to finding the probability to our problem is to now subtract our areas:

.7881–.0446 = .7435

So the answer to our problem is:

The probability that the profits for the next quarter will lie between $100 million and $150 million is .7435.

I hope my explanation was very helpful, good luck on the final everyone! 🙂