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?
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
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 = 0.8
2. z = 100-134/20
z = -1.7
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.
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! 🙂