Women’s heights are normally distributed with a mean of 162 cm and standard deviation of 16 cm.

a. Define an random variable, X, and describe its full distribution including the mean and variance.
b. What percentage of heights are greater than 180 cm ?
c. What height is at the 90th percentile (i.e. height separating the lower 90% from the upper 10%)?
d. What height is at the 40th percentile?
e. If five students are chosen at random, what is the probability that none of them will be in the 90th percentile or higher?

1 answer

a. You already have that information given.

b. Z = (score-mean)/SD

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to the Z score.

c, d, e. Use same table.

e. Probability of all events occurring = product of the individual probabilities.