Answer:
8
Explanation:
First, we need to find the mean, so the sum of all values divided by the number of values is equal to:
[tex]\begin{gathered} \operatorname{mean}\text{ = }\frac{87+63+39+67+66+63+62+67+66}{9} \\ \operatorname{mean}\text{ = }\frac{580}{9} \\ \operatorname{mean}\text{ = 64.44} \end{gathered}[/tex]Then, we need to find the population standard deviation, so we need to find the square of the difference between each value and the mean:
(87 - 64.44)² = 508.75
(63 - 64.44)² = 2.08
(39 - 64.44)² = 647.41
(67 - 64.44)² = 6.53
(66 - 64.44)² = 2.41
(63 - 64.44)² = 2.08
(62 - 64.44)² = 5.97
(67 - 64.44)² = 6.53
(66 - 64.44)² =2.41
Now, the standard deviation will be the square root of the sum of these values divided by the number of values, so:
[tex]\begin{gathered} s=\sqrt[]{\frac{508.75+2.08+647.41+6.53+2.41+2.08+5.97+6.53+2.41}{9}} \\ s=\sqrt[]{\frac{1184.22}{9}} \\ s=\sqrt[]{131.58} \\ s=11.47 \end{gathered}[/tex]Therefore, the data that is within 2 population standard deviations to the mean is the data that is located within the following limits:
mean + 2s = 64.44 + 2(11.47) = 87.38
mean - 2s = 64.44 - 2(11.47) = 41.5
So, from the 9 values, 8 are within 2 population standard deviations of the mean.
Therefore, the answer is 8.