Question

1. A Normal random variable X has mean 20 and standard deviation 4. Calculate the probability that specific values of X exceed 26.
2. Calculate the 36th percentile of a Standard Normal random variable.
3. 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.
4. 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

Anso-ceiven X has a normal distribution with mean-20 and sd-4 PIX >26) = PIX-14 > 26—20) > piz >105). lusing a distribution = 0.0668 at table ) (8) ce need to calculcate the 36th percentile of a standard - Normal random variable - we need to find the a-score for a > which the probability of scoring equal oo > less than a es 0.36 15 MINIC tl + 2 2 le P(Z <z) = 0.36 > using z-distribution terble, Z Z-0.3585 - CS Seanned with CamScanner