Question

Suppose that the lengths of human pregnancies are normally distributed with a mean of 268 days and a standard deviation of 16 days. Complete the following statements.

Answer 1

(a) The empirical rule says that about 95% of all values lie within 2 standard deviation of the mean. Thus;

Thus;

`\begin{gathered} z_1=-2=(x_1-268)/(16) \\ \\ x_1=268-32 \\ \\ x_1=236 \\ \\ z_2=2=(x_2-268)/(16) \\ \\ x_2=268+32 \\ \\ x_2=300 \end{gathered}`

ANSWER: Approximately 95% of pregnancies have lengths between 236 days and 300 days.

(b)

`\begin{gathered} x_1=252 \\ \\ z_1=(252-268)/(16) \\ \\ z_1=-1 \\ \\ x_2=284 \\ \\ z_2=(284-268)/(16) \\ \\ z_2=1 \end{gathered}`

Thus;

[tex]\begin{gathered} P(-1