Stat problems for Monday, Feb 15

This looks a lot like the problems from last Friday but today you're going to use our new online normal calculator to do the computations, rather than looking up the results in a table. There's also a third, data driven problem.

Be sure to use the calculator for the HW, since it can give more precise answers.

1. Compute the following probabilities for a random variable $Z$ that has a standard normal distribution.
   1. $P(Z < 1.234)$
   2. $P(Z > 1.234)$
   3. $P(-0.4321 < Z < 1.234)$
2. Suppose that $X$ is normally distributed with a mean of 3.14 and a standard deviation of 2.78. Compute
   1. $P(X < 1.234)$
   2. $P(X > 1.234)$
   3. $P(-0.4321 < X < 1.234)$
3. Suppose that the height of men in the US is normally distributed with an average of $70.25$ inches with a standard deviation of $3$ inches. Use a normal distribution to estimate the proportion of men who are more than $75$ inches tall.