The length of time to find it takes to find a parking space

The length of time to find 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. If the mean is significantly greater than the standard deviation, which of the following statements is true?

I. The data cannot follow the uniform distribution.

II. The data cannot follow the exponential distribution..

III. The data cannot follow the normal distribution.

a. I only

b. II only

c. III only

d. I, II, and III

Can someone tell me if it\'s a, b, c, or d and explain why? Thanks!

Solution

The answer is I only because:

for a normal distribution, the mean is independent of the standard deviation.

for an exponential distribution, mean and sd have the same value.

for a uniform distribution, the formula is 1/(a + b) for mean and the standard deviation formula is (b - a) /sqrt(12). No matter what, the standard deviation is greater than the mean for any values a and b.