Question

Please help

The lengths of pregnancy terms for a particular species of mammal are nearly normally distributed about a mean pregnancy length with a standard deviation of 17 days. About what percentage of births would be expected to occur within 51 days of the mean pregnancy​ length?

Answer 1

About 99.7% of births would be expected to occur within 51 days of the mean pregnancy​ length

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:

Standard deviation = 17.

About what percentage of births would be expected to occur within 51 days of the mean pregnancy​ length?

51/17 = 3.

So, within 3 standard deviations of the mean.

About 99.7% of births would be expected to occur within 51 days of the mean pregnancy​ length