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 6.5 minutes and a standard deviation of 1 minute. Find the probability that a randomly selected college student will find a parking spot in the library parking lot in less than 6.0 minutes.

Answer 1

Answer: P(X<6) = 0.3085 or 30.85%

Step-by-step explanation: Determine, first, z-score:

$z = \frac{x-\mu}{\sigma}$

x is a random variable for time a student takes to find a spot, in this case, x=6:

$z = \frac{6-6.5}{1}$

z = -0.5

Using z-score table, find z-score:

P(X<6) = P(z< -0.5)

P(X<6) = 0.3085

Probability of finding a parking spot in less than 6 minutes is approximately 30.85%.