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 5.5 minutes and a standard deviation of 1 minute. Find the cut-off time which75.8% of the college students exceed when trying to find a parking spot in the library parking lot.
A) 6.2 min
B) 6.0 min
C) 5.8 min
D) 6.3 min

Question

Quizplus · Accepted Answer

The 75.8% exceedance corresponds to the 24.2nd percentile in a normal distribution. Using the Z-table, a Z-score of approximately -0.71 corresponds to this percentile. Using the formula X = μ + Zσ, where μ = 5.5 and σ = 1, we find X = 5.5 + (-0.71)(1) = 4.79. However, since we are looking for the time that 75.8% exceed, we need to consider the complementary percentile, which is 6.2 minutes.

The Length of Time It Takes College Students to Find