Question

1. For a Standard Normal random variable Z, calculate the probability P(-0.25 < Z < 0.25).
2. For a Standard Normal random variable Z, calculate the probability P(-0.32 < Z < 0.32).
3. For a Standard Normal random variable Z, calculate the probability P(-0.43 < Z < 0.43).
4. Calculate the z-score of the specific value x = 26 of a Normal random variable X that has mean 20 and standard deviation 4.
5. A Normal random variable X has mean 20 and standard deviation 4. Calculate the probability that specific values of X exceed 26.
6. Calculate the 36th percentile of a Standard Normal random variable.
7. A Standard Normal random variable Z falls within an interval of values centered around zero, that is the interval -z to z, with probability 0.6. Calculate the value of z that defines that interval.
8. A truck makes daily round trips between Charlotte and Atlanta. On 30 percent of all days the round trip takes at most 480 minutes, and the standard deviation of round trip times is 40 minutes. The round trip time is a Normally distributed random variable. Calculate the mean round trip time.

Answer 1

1)

This is a normal distribution question with

This implies that
P(-0.25 < z < 0.25) = 0.1974

2)

This is a normal distribution question with

This implies that
P(-0.32 < z < 0.32) = 0.251

3)

This is a normal distribution question with

​​​​​​​

This implies that

P(-0.43 < z < 0.43) = 0.3328

4)

This is a normal distribution question with

​​​​​​​

x = 26

The z-score at x = 26.0 is,

z = 1.5