Question

The length of time it takes to find a parking space at 9 A.M. follows a normal distribution with a mean of 7 minutes and a standard deviation of 3 minutes. Based upon the above 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.

Answer 1

Answer:

a. Yes

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$, the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

If the absolute value of the z-score is 2 or larger, X is considered a surprising outcome.

In this question:

$\mu = 7, \sigma = 3$

Would you be surprised if it took less than one minute to find a parking space?

We have to find the z-score when X = 1. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{1 - 7}{3}$

$Z = -2$

Since Z = -2, the correct answer is:

a. Yes