Question

Pregnancy lengths are normally distributed with a mean of 280 days and a standard deviation of 20 days. Find the probability that if a sample of 50 pregnancies are chosen at random that the mean length is less than 270 days.

Answer 1

Solution :

Given that,

mean = = 280

standard deviation = = 20

n = 50

= 280

=  / n = 20 / 50=2.828

P( <270 ) = P[( - ) / < (270-280) /2.828 ]

= P(z < -3.54)

Using z table  

= 0.0002

probability= 0.0002