Question: A population is normally distributed with a mean of 25 and a standard deviation of 5. (2 points each except part e ) Show your work.

a. If a piece of datum is randomly taken from this distribution, what is the probability that it is less than 20?

b. If a piece of datum is randomly taken from this distribution, what is the probability that a value of X is between 20 and 35?

c. What value represents the 90^th percentile of the distribution?

d . Between what two values will the middle 80% of the data fall?

e. If a sample of 4 pieces of data are taken from this distribution, what is the probability the mean will be less than 20? (5 points)