The length of time it takes college students to find a parking spot in the library parking lot follows a normaldistribution with a mean of 6.5 minutes and a standard deviation of 1 minute. Find the probability that arandomly selected college student will take between 5.0 and 7.5 minutes to find a parking spot in the librarylot.
A) 0.7745
B) 0.4938
C) 0.0919
D) 0.2255

Question

Quizplus · Accepted Answer

To find the probability that a time is between 5.0 and 7.5 minutes, we use the Z-score formula: Z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation. For X = 5.0, Z = (5.0 - 6.5) / 1 = -1.5. For X = 7.5, Z = (7.5 - 6.5) / 1 = 1.0. Looking these Z-scores up in a standard normal distribution table or using a calculator, the probability of Z being between -1.5 and 1.0 is approximately 0.7745.

The Length of Time It Takes College Students to Find