Question

Suppose we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute.

What is the probability that a randomly selected college student will take between 2.5 and 4.5 minutes to find a parking spot in the library parking lot?

Answer 1

So the probability between 2 and 4.5 = 0.8413 – 0.0668

= 0.7745

Explanation:

mean = 3.5

standard deviation = 1 minute

Apply z statistic

for 4.5 minutes and 2 minutes

Calculate z for 4.5 minutes

z= (4.5-3.5)/1

= 1.0

Calculate z for 2 minutes

(2-3.5)/1 = -1.5

z= 1 is 0.8413

z= - 1.5 is 0.0668

So the probability between 2 and 4.5 = 0.8413 – 0.0668

= 0.7745