Question

The length of human pregnancies are normally distributed with a mean of 281.9 days and a standard deviation of 11.4 days.

a) Find the probability of a pregnancy lasting more than 258 days ( that is premature status).

b) Draw the distribution (Label the x value/or z value) and shade the area we are concerned with and calculate the probability.

c) Of 500 pregnant women, about how many would you expect to be pregnant for a length of more than 258 days? (Round to the nearest woman)

Answer 1

Part a)

P ( X > 258 ) = 1 - P ( X < 258 )
Standardizing the value

Z = ( 258 - 281.9 ) / 11.4
Z = -2.1

P ( Z > -2.1 )
P ( X > 258 ) = 1 - P ( Z < -2.1 )
P ( X > 258 ) = 1 - 0.0179
P ( X > 258 ) = 0.9821

Part b)

Part c)

P ( X > 258 ) = 0.9821

500 * 0.9821 = 491.05   491.