Question

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 7.0 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.

Answer 1

Let the cutoff time exceeded by 75.8% of the college students exceed when trying to find a parking spot in the library parking lot be A

P(X < A) = P(Z < (A - mean)/standard deviation)

Here, Mean = 7.0 minutes

Standard deviation = 1 minute

P(X > A) = 0.758

P(X < A) = 1 - 0.758 = 0.242

P(Z < (A - 7)/1) = 0.242

From standard normal distribution table, the the value of Z corresponding to probability of 0.2420

(A - 7)/1 = -0.7

A = 6.3 minutes

= 6 minutes and 18 seconds