Question

The links of pregnancy terms for a particular species of mammal are nearly normally distributed about a mean pregnancy length with a standard deviation of 12 days. About what percentage of births would be expected to occur within 36 days of the mean pregnancy length?

a) 16%
b) 34%
c) 68%
d) 84%

Answer 1

Using the empirical rule for a normal distribution, approximately 68% of births are expected to occur within 36 days of the mean pregnancy length for the mammal species in question.

Step-by-step explanation:

The question asks us to find the percentage of births expected to occur within 36 days of the mean pregnancy length for a mammalian species, where pregnancy lengths are normally distributed with a given standard deviation. Applying the empirical rule, also known as the 68-95-99.7 rule, to a normal distribution, we can determine the percentage as follows:

Since 36 days equals 3 standard deviations (where 1 standard deviation = 12 days), approximately 68% of the data lies within ±3 standard deviations from the mean. Therefore, the percentage of births expected to occur within 36 days of the mean is about 68%.

The correct answer to the student's question is therefore (c) 68%.