Question

The length of human pregnancies from conception to birth varies according to a distribution that is approximately Normal with mean 266 days and standard deviation 16 days,

The probability that the average pregnancy length for six randomly chosen women exceeds 270 days is about

Answer 1

0.27

Explanation:

The variance of the distribution of pregnancy lengths is 16x16 = 256.

The sum of pregnancy lengths of 6 randomly chosen women follows a normal distribution with mean = 6x266 = 1596 and variance = 6x256 = 1536.

Compute the probability that the sum exceeds 6x270 = 1620.

P(X>1620) = 1-Φ(
`(1620-\mu)/(\sigma)`) = 1-Φ(
`(1620-1596)/(√(1536))`) = 0.27

where Φ is the c.d.f of the standard normal distribution,

μ is mean and σ is the standard deviation of the sum of 6 pregnancy lengths.