Question

The lengths of a particular​ animal's pregnancies are approximately normally​ distributed, with mean muequals268 days and standard deviation sigmaequals20 days. ​(a) What proportion of pregnancies lasts more than 293 ​days? ​(b) What proportion of pregnancies lasts between 233 and 278 ​days? ​(c) What is the probability that a randomly selected pregnancy lasts no more than 263 ​days? ​(d) A​ "very preterm" baby is one whose gestation period is less than 238 days. Are very preterm babies​ unusual?

Answer 1

Solution :

Given that ,

a) P(x > 293) = 1 - p( x< 293 )

=1- p P[(x - ) / < (293 - 268) / 20 ]

=1- P(z < 1.25)

= 1 - 0.8944

= 0.1056

b) P(233 < x < 278 ) = P[(233 - 268)/ 20) < (x - ) /  < (278 - 268) / 20) ]

= P(-1.75 < z < 0.50)

= P(z < 0.50) - P(z < -1.75)

Using z table,

= 0.6915 - 0.0401

= 0.6514

c) P(x < 263)

= P[(x - ) / < (263 - 268) / 20]

= P(z < -0.25)

Using z table,

= 0.4013

d) P(x < 238)

= P[(x - ) / < (238 - 268) / 20]

= P(z < -1.50)

Using z table,

= 0.0668

It is not unusual, because probability is more than 5%