Question

Suppose that many large samples are taken from a population and that the

sample proportions are normally distributed, with a mean of 0.22 and a
standard deviation of 0.029.99.7% of the sample proportions will fall within
which of the following intervals?

Answer 1

99.7% of the sample proportions will fall between 0.133 and 0.307.

Explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 0.22

Standard deviation = 0.029

99.7% of the sample proportions will fall within which of the following intervals?

Within 3 standard deviations of the mean.

Lower end: 0.22 - 3*0.029 = 0.133

Upper end: 0.22 + 3*0.029 = 0.307

99.7% of the sample proportions will fall between 0.133 and 0.307.