Find the Value of a Normal Random Variable
-The length of time it takes college students to find a parking spot in the library parking lot follows a normal distribution with a mean of 4.0 minutes and a standard deviation of 1 minute. Find the cut-off time which 75.8% of the college students exceed when trying to find a parking spot in the library parking lot.
A) 4.7 min
B) 4.5 min
C) 4.3 min
D) 4.8 min

Question

Quizplus · Accepted Answer

To find the cut-off time which 75.8% of students exceed, we need to find the 24.2th percentile (100% - 75.8%) of the normal distribution. Using the Z-table, the Z-score for 0.242 is approximately -0.7. Using the formula X = μ + Zσ, where μ = 4.0 and σ = 1, we get X = 4.0 + (-0.7)(1) = 3.3. However, since the question asks for the time that 75.8% exceed, we need to find the complement, which is 4.7 minutes.