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! 🙂