Question

The amount spent per month by employees for parking at a municipal lot is normally distributed with a mean of $320 and a standard deviation of $40. About what percentage of the observations lie between $280 and $360 ?

Answer 1

To find the percentage of observations between $280 and $360 for parking costs, calculate the z-scores for both values and use the standard normal distribution table, which typically shows that about 68% of data falls within one standard deviation from the mean in a normal distribution.

Step-by-step explanation:

The question is asking for the percentage of employees whose parking costs fall between $280 and $360 given that the parking costs follow a normal distribution with a mean of $320 and a standard deviation of $40. To address this, one would use the properties of the normal distribution, specifically standard scores (also known as z-scores), and consult a standard normal distribution table or use a calculator with statistical functions.

First, you calculate the z-scores for both values $280 and $360:

Z for $280 = (280 - 320) / 40 = -1

Z for $360 = (360 - 320) / 40 = 1

Using a standard normal distribution table or calculator, you can find the percentage of values falling between a z-score of -1 and 1. Typically, this range encompasses approximately 68% of data in a normal distribution.