The driver's seat in most vehicles is set to comfortably fit a person who is at least 159 cm tall. The distribution of heights of adult women is approximately normal with a mean of 161.5 cm and a standard deviation of 6.3 cm. Determine the percentage of women who can be expected to be uncomfortable in the driver's seat of their car without some sort of an adjustment.
A) 0.3446.
B) 0.1554.
C) 0.6554.
D) 0.8446

Question

Quizplus · Accepted Answer

The percentage of women who are uncomfortable in the driver's seat is the percentage who are less than 159 cm tall. This is the area under the normal curve to the left of 159 cm. Using the standard normal distribution, we find that the z-score for 159 cm is (159 - 161.5) / 6.3 = -0.4. The area to the left of -0.4 is 0.3446, so the percentage of women who are uncomfortable in the driver's seat is 34.46%.

The Driver's Seat in Most Vehicles Is Set to Comfortably