If we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute,75.8% of the college students will take more than how many minutes when trying to find a parking spot in the library parking lot?
A)2.8 minutes
B)3.2 minutes
C)3.4 minutes
D)4.2 minutes

Question

Quizplus · Accepted Answer

The percentage of students who take more than a certain time to find a parking spot corresponds to the area under the normal distribution curve to the right of that time. Given that 75.8% of students take more than a certain time, this means that 24.2% (100% - 75.8%) of the area under the curve is to the left of this time. Looking up 24.2% in a standard normal distribution table or using a calculator, we find that it corresponds to a Z-score of approximately -0.7. Using the formula for converting a Z-score to an original score (X = μ + Zσ), where μ is the mean and σ is the standard deviation, we get X = 3.5 + (-0.7)(1) = 2.8 minutes.

If We Know That the Length of Time It Takes