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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.)

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.

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