Question

the sitting height (from the bottom of the seat to the top of the person's head) of female drivers is normally distributed with a mean of 34 inches and a standard deviation of 1.4 inches as shown below. If a car company designs a vehicle so that the roof is 34 inches from the bottom of the seat, what percentage of women would not fit in the driver's seat? A. 40% B. 50% C. 50.1% D. 60%

Answer 1

B; 50%

Explanation:

Here, we want to calculate the percentage of women that will not fit in the driver’s seat

We proceed as follows;

We start with calculating the z-score of this;

That would be ;

(x-mean)/SD

in this case;

x = 34 inches

mean = 34 inches

SD = 1.4 inches

Thus, we have that;

(34-34)/1.4 = 0/1.4 = 0

when z-score is 0, we are at the center of the distribution

A z-score of 0 corresponds to exactly 50%