# Computing Normal Probabilities with a Given Z Score

1. Given that z is a standard normal random variable, compute the following probabilities.

a. p (z = 2.0)

b. p (z ≥ 1.4)

c. p (-1.0 < z < 0.5)

d. p (1.0 < z < 1.2)

2. The time needed to drive from city A to city B is normally distributed with a mean of 180 minutes and standard deviation of 20 minutes.

a. What is the probability that a person will drive from city A to city B in three hours or more?

b. What is the probability that a person will drive from city A to city B in more than 140 minutes?

c. What is the probability that a person will drive from city A to city B in exactly three hours?

d. What is the probability that a person will drive from city A to city B in less than 2.5 hours?

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Answers

a. p (z = 2.0)

P (Z = 2.0) = 0, since for a continuous random ...

#### Solution Summary

The solution provides a step by step method for the calculation of probability using a given Z score. The formula for the calculation and interpretations of the results are also included.