Question

The lengths of a particular​ animal's pregnancies are approximately normally​ distributed, with mean μ= 272

days and standard deviation σ= 88 days.

​(a) What proportion of pregnancies lasts more than 286 ​days?

​(b) What proportion of pregnancies lasts between 262 and 274 ​days?

​(c) What is the probability that a randomly selected pregnancy lasts no more than 264​days?

​(d) A​ "very preterm" baby is one whose gestation period is less than 260 days. Are very preterm babies​ unusual?

Answer 1

Solution :

Given that ,

mean = = 272

standard deviation = = 88

a) P(x > 286 ) = 1 - p( x< 286)

=1- p [(x - ) / < (286 -272) /88 ]

=1- P(z < 0.16 )

= 1 - 0.5636 = 0.4364

proportion = 0.4364

b)

P( 262< x < 274 ) = P[(262 -272 )/88 ) < (x - ) /  < (274 - 272 ) /88 ) ]

= P( -0.11< z < 0.02 )

= P(z < 0.02 ) - P(z <-0.11 )

Using standard normal table

= 0.508 - 0.4562 = 0.0518

Probability = 0.0518

c)

P(x 264 )

= P[(x - ) / (264 -272 ) /88 ]

= P(z -0.09 )

= 0.4641

probability = 0.4641

d)

P(x < 260 ) = P[(x - ) / < (260 -272) /88 ]

= P(z < -0.14)

= 0.4443

probability =0.4443

A​ "very preterm" babyies are not unusual, because probability is gretar than 0.05.