Stats homework please help

Question

1. The speeds of vehicles are normally distributed , with a mean of 67 miles per hour and a standard deviation of 4 miles per hour. What vehicle speed corresponds to the 30th percentile?

(a) 65.8 (b) 68.2 (c) 64.5 (d) 64.9

1. Students’ scores on a final exam had a mean of 79. If a student had a z-score of 0, which one of the following represents her exam score.

(a) 73 (b) 79 (c) 81 (d) not enough information

Answer 1

x = speed of vehicle:

Using standard normal probabilities table:

P(z < -0.524) = 0.30, so z = -0.524 corresponds to 30th percentile.

z = (x - mean)/standard deviation

-0.524 = (x - mean)/standard deviation

-0.524 = (x - 67)/4

A z score of 0 means x is equal to the mean (79) (b)

x = 64.904 ~ 64.9 (d)