Question

The length of time to find a parking spot on the UW campus is normally distributed with a mean of 4.75 minutes and a standard deviation of 1.35 minutes. Find the probability than a randomly selected driver takes less than 2 minutes to find a parking spot on the UW campus. Round your answer to three decimal places.

Answer 1

Answer: 0.0208

Explanation:

Given: The length of time to find a parking spot on the UW campus is normally distributed with a mean of 4.75 minutes and a standard deviation of 1.35 minutes.

Let x = time taken to find parking spot

The probability that a randomly selected driver takes less than 2 minutes to find a parking spot on the UW campus will be :

`P(x<2)=P((x-\mu)/(\sigma)<(2-4.75)/(1.35))\\\\=P(Z<-2.037)\ \ \ [z=(x-\mu)/(\sigma)]\\\\=1-P(Z<2.037)\\\\=1- 0.9792=0.0208\ \ \ \text{[By p-value table]}`

Hence, the probability than a randomly selected driver takes less than 2 minutes to find a parking spot on the UW campus.= 0.0208