Question

For the following data set, calculate the percentage of data points that fall within one standard deviation of the mean, and compare the result to the expected percentage of a normal distribution.

{70, 85, 84, 83, 96, 74, 66, 99, 84, 81}

A.
50%; This percentage is lower than expected in a normal distribution.

B.
60%; This percentage is lower than expected in a normal distribution.

C.
70%; This percentage is close to the expected percentage in a normal distribution.

D.
80%; This percentage is higher than expected in a normal distribution.

Answer 1

Answer: B.) 60%; This percentage is lower than expected in a normal distribution.

Hope this helps :)

Answer 2

Answer: B.

Explanation:

mean of {70, 85, 84, 83, 96, 74, 66, 99, 84, 81} is 82.2

population standard deviation is 9.8367

sample standard deviation is 10.369

Problem says nothing about random sample from a population, so the given values must be the whole population, so standard deviation is 9.8367 and not 10.369.

range for "one sigma" is 82.2-9.8 to 82.2+9.8 = 72.4 to 92.0

two data points are below, two are above. that is 40% of 10 data points outside, 60% inside.

Answer is B