Question

The lengths of a particular​ animal's pregnancies are approximately normally​ distributed, with mean muequals257 days and standard deviation sigma equals20 days. ​(a) What proportion of pregnancies lasts more than 267 ​days? ​(b) What proportion of pregnancies lasts between 242 and 272 ​days? ​(c) What is the probability that a randomly selected pregnancy lasts no more than 217 ​days? ​(d) A​ "very preterm" baby is one whose gestation period is less than 227 days. Are very preterm babies​ unusual? ​(a) The proportion of pregnancies that last more than 267 days is nothing.

Answer 1

Solution :

Given that ,

mean = = 257 days

standard deviation = = 20 days

a) P(x > 267) = 1 - p( x< 267)

=1- p P[(x - ) / < (267 - 257) /20 ]

=1- P(z < 0.50)

Using z table,

= 1 - 0.6915

= 0.3085

b) P(242 < x < 272) = P[(242 - 257)/ 20) < (x - ) /  < (272 - 257) / 20) ]

= P(-0.75 < z < 0.75)

= P(z < 0.75) - P(z < -0.75)

Using z table,

= 0.7734 - 0.2266

= 0.5468

c) P(x < 217) = P[(x - ) / < (217 - 257) /20 ]

= P(z < -2.00)

Using z table,

=0.0228

d) P(x < 227) = P[(x - ) / < (227 - 257) /20 ]

= P(z < -1.50)

Using z table,

=0.0668

No, it would be not unusual because probability is more than 5%.