# Stat 185 - Problem sheet

#### Friday, August 28

We’re going to practice a few problems in groups today. These should all help get you ready for the HW that’s due next Monday. The last one will also reinforce the importance of the normal distribution.

You should solve these problems together and then your group should send me *one* set of solutions as a private message on the forum. I’ll jump around and see how your doing.

### The problems

- Suppose that
*U* is a continuous, uniformly distributed random variable on the interval [0, 4]. What are
*P*(1 < *U* < 2.5) and
*P*(*U* > 3)?

- Suppose
*Y* has the distribution shown below. What is *P*(*Y* > 1)?

- The histogram for the heights of men from our CDC data set is shown below. The curve is the normal curve that has the same mean
*μ* and standard deviation *σ* as the data. The numbers on the horizontal axis show the locations of *μ* − 3*σ*, *μ* − 2*σ*, *μ* − *σ*, *μ*, *μ* + *σ*, *μ* + 2*σ*, *μ* + 3*σ*. Based on that curve and the basic rules of the normal distribution, what is the percentage of men whose height is less than 73.26 inches?