Question

THE PROBLEM:

Kip had to renew his license and while sitting at the DMV he surveyed everyone else there, asking them their age. The data turned out to have normal distribution, the mean age was 41, and the standard deviation was 5.



1. On paper, make a bell curve with the appropriate values listed on the axis below. Show your teacher.

2. What % of people were below 31 years old?

3. What % of people were above 31 years old?

4. What % of people were between 41 and 46?

5. About what % of people were older than Kip (he's 38 years old)?

Answer 1

1. To make a bell curve (a normal distribution) with a mean of 41 and a standard deviation of 5, we can use the following values on the x-axis:

x = 21, 26, 31, 36, 41, 46, 51, 56, 61

These values are symmetric around the mean of 41, and each value is one standard deviation away from the mean.

On the y-axis, we can mark the percentage of people in each interval, which is calculated using the area under the curve. The total area under the curve is 100%.

2. To find the percentage of people who were below 31 years old, we need to calculate the area under the curve to the left of x = 31. Using a standard normal distribution table or calculator, we can find this area to be approximately 0.0228, or 2.28%.

So, about 2.28% of people were below 31 years old.

3. To find the percentage of people who were above 31 years old, we can subtract the percentage of people below 31 years old from 100%.

100% - 2.28% = 97.72%

So, about 97.72% of people were above 31 years old.

4. To find the percentage of people between 41 and 46 years old, we need to calculate the area under the curve between x = 41 and x = 46. Using a standard normal distribution table or calculator, we can find this area to be approximately 0.3413, or 34.13%.

So, about 34.13% of people were between 41 and 46 years old.

5. To find the percentage of people older than Kip (who is 38 years old), we need to calculate the area under the curve to the right of x = 38. Using a standard normal distribution table or calculator, we can find this area to be approximately 0.6306, or 63.06%.

So, about 63.06% of people were older than Kip.

Explanation: