Exercise 37 Page 745

We are asked to determine which distribution, A or B, has more data values below 40. To do that we will first find the percentage of values that are below 40 for Distribution A.

Distribution A

We are told that Distribution A has a mean of 40 and a standard deviation of 2.4.

Notice that half (50 %) of the values are at or below 40.

Distribution A has 50 values. Therefore, 50 % of the 50 values are at or below 40. Let's evaluate that number.

We found that for Distribution A 25 values are at or below 40.

Distribution B

Distribution B has also a mean of 40. However, the standard deviation is equal to 2.8.

Similarly to before, half (50 %) of the values are at or below 40.

Distribution B has 30 values. Therefore, 50 % of the 30 values are at or below 40. Let's evaluate that number.

We found that for Distribution B 15 values are at or below 40. Let's summarize our results.

We can see that Distribution A has more values at or below 40.