# Probabilities

1.Find the probabilities for the standard normal random variable z: P(-1.55<z<.44)

2. Find zo such that P(-zo<z<zo)=.99

3. A normal random variable x has mean =1.20 and standard deviation =.15. Find the probability of the x value. 1.35<x<1.50 b. x>1.38

4. Assume the heights of men have a mean of 69 inches with a standard deviation 3.5 inches.

a. What proportion of all mean with be taller than 6'

b. what is the probability that a randomly selected man will be between 5'8 and 6'1

c. Is 6' tall a unusual height

5.A study of elevator occupancies indicates that if eight people occupy the elevator, the probability distribution of the total weight of the eight people has a mean equal to 1200 pounds and a variance equal to 9800 lbs. What is the probability that the total weight of eight people exceeds 1300 pounds? 1500 pounds? (Assume that the probability distribution is approximately normal.)

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#### Solution Preview

1. P(-1.55<z<0.44)=0.6095 or 60.95% This can be done by a graph calculator.

2. Since d=1 and P(-3d<z<3d)=0.997. Thus we can select z0=2.7

P(-2.7<z<2.7)=0.9931=0.99

3. ...

#### Solution Summary

The solution answers the question(s) below.