Question

The lengths of a particular​ animal's pregnancies are approximately normally​ distributed, with mean μ=267 days and standard deviation σ=16 days.

​(a) What proportion of pregnancies lasts more than 275 days?

​(b) What proportion of pregnancies lasts between 263 and 271 days?

​(c) What is the probability that a randomly selected pregnancy lasts no more than 247 days?

​(d) A​ "very preterm" baby is one whose gestation period is less than 243 days. Are very preterm babies​ unusual?

Answer 1

Solution :

Given that ,

mean = = 267

standard deviation = = 16

a) P(x > 275) = 1 - p( x< 275)

=1- p P[(x - ) / < (275 - 267) / 16]

=1- P(z < 0.50)

Using z table,

= 1 - 0.6915

= 0.3085

b) P(263 < x <271 ) = P[(263 - 267)/ 16 ) < (x - ) /  < (271 - 267) /16 ) ]

= P(-0.25 < z < 0.25)

= P(z < 0.25) - P(z < -0.25)

Using z table,

= 0.5987 - 0.4013

= 0.1974

c) P(x < 247)

= P[(x - ) / < (247 - 267) / 16]

= P(z < -1.25)

Using z table,

= 0.1056

d) P(x < 243)

= P[(x - ) / < (243 - 267) / 16]

= P(z < -1.50)

Using z table,

= 0.0668

It is not unusual because probability more than 5%