The time it takes Jessica to bicycle to school is normally distributed with mean 15 minutes and variance 4. Jessica has to be at school at 8:00 am. What time should she leave her house so she will be late only 4% of the time?
A) 15 minutes before 8:00
B) 11.5 minutes before 8:00
C) 22 minutes before 8:00
D) 18.5 minutes before 8:00
E) 10.5 minutes before 8:00

Question

Quizplus · Accepted Answer

First, we need to find the standard deviation, which is the square root of the variance:

SD = sqrt(4) = 2

Next, we need to find the z-score for the 4th percentile, which is -1.75 (using a z-table or calculator).

Finally, we can use the formula:

z = (x - mu) / SD

-1.75 = (x - 15) / 2

Solving for x, we get:

x = 11.5

Therefore, Jessica should leave her house 11.5 minutes before 8:00 am, which is answer choice D.

The Time It Takes Jessica to Bicycle to School Is