Question

Lengths of pregnancies of women are normally distributed with a mean of 266 days and a standard deviation of 16 days.

What percentage to the nearest hundredth of children are born from pregnancies lasting more than 274 days?

What percentage to the nearest hundredth of children are born from pregnancies lasting less than 246 days?

Answer 1

Explanation:

Use the formula for a normal dist.

⊕ = sigma

∪ = standard deviation, mu

f(x) = 1 / (⊕*
`√(2\pi )`)*e^(-1/2*(x-∪/⊕)^2)

A) f(274) = 1 / (16*
`√(2\pi )`)*e^(-1/2*(274-266/16)^2)

= 0.022

B F(246) = 1 / (16*
`√(2\pi )`)*e^(-1/2*(246-266/16)^2)

= 0.017