In this article, (and video above), we’re going to use a normal distribution to determine the probability of a curve. This question forms part of the probability & statistics section of the FE Exam and will give you a better understanding of what you can expect during the exam.

**Question:**

Given a normal distribution of quantity x, where n(x) represents the unit normal distribution function, what is the probability that a given sample quantity, x1, will lie between x = x0 and x = x2?

**Solution:**

The probability that an event will lie within a certain range of an independent variable is equal to the area under the normal distribution curve for that range of the independent variable. Since integration gives the area under a curve, the area under the normal distribution curve, n(x), between x0 and x2 is given by the expression shown in option (A). For more details, please see the video at the top of this post.

**Answer:**

The correct answer is A.

**This Episode Is Brought to You by PPI**

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I hope you found this week’s FE Environmental engineering exam prep question helpful. In upcoming articles, I will answer more FE Exam questions and run through more practice problems. We publish videos bi-weekly on our Pass the FE Exam YouTube Channel. Be sure to visit our page here and click the subscribe button as you’ll get expert tips and tricks – to ensure your best success – that you can’t get anywhere else. Believe me, you won’t want to miss a single video.

Lastly, I encourage you to ask questions in the comments of the videos or here on this page and I’ll read and respond to them in future videos. So, if there’s a specific topic you want me to cover or answer, we have you covered.

I’ll see you next week.

Anthony Fasano, P.E.

Engineering Management Institute

*Author of Engineer Your Own Success*

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