Normal deviation question!?

Question

The length of time it takes to find a parking space at 9 A.M. follows a normal distribution with a mean of five minutes and a standard deviation of two minutes.
Based upon the given information and numerically justified, would you be surprised if it took less than one minute to find a parking space?
a. Yes
b. No
c. Unable to determine

I need some help with this question, I would prefer the steps how to do it over the answers so that I can understand it better. Thanks.

Mike G · Answer

σ =  2
μ = 5
z(1) = (1-5)/2 = -2
P(z<-2) = 2.28% (From the tables or z-score calculator)
P(z<-2) = 2.25% (Using the Empirical Rule)
So only 2.28% of people would take less than 1 minute to park
Answer a.

Some Body · Answer

The mean is 5 minutes and the standard deviation is 2 minutes.

Since this follows a normal distribution, we know that two standard deviations below the mean is 5 - 2*2 = 1 minute.

As a general rule, anything outside plus or minus two standard deviations is considered to be statistically significant, since only 5% of the distribution is outside of this range.  So yes, it would be unlikely to find a parking space in less than one minute.

Normal deviation question!?

Trending Questions