Question

The lengths of a particular​ animal's pregnancies are approximately normally​ distributed, with mean μ=252 days and standard deviation σ=16 days.

​(a) What proportion of pregnancies lasts more than 272 ​days?

​(b) What proportion of pregnancies lasts between 248 and 260 ​days?

​(c) What is the probability that a randomly selected pregnancy lasts no more than 224 ​days?

​(d) A​ "very preterm" baby is one whose gestation period is less than 216 days. Are very preterm babies​ unusual?

Answer 1

Solution :

Given that ,

mean = = 252

standard deviation = = 16

(a)

P(x > 272) = 1 - P(x < 272)

= 1 - P[(x - ) / < (272 - 252) / 16)

= 1 - P(z < 1.25)

= 1 - 0.8944

= 0.1056

Proportion = 0.1056

(b)

P(248 < x < 260) = P[(248 - 252)/ 16) < (x - ) /  < (260 - 252) / 16) ]

= P(-0.25 < z < 0.5)

= P(z < 0.5) - P(z < -0.25)

= 0.6915 - 0.4013

= 0.2902

Proportion = 0.2902

(c)

P(x 224)

= P[(x - ) / (224 - 252) / 16]

= P(z -1.75)

= 0.0401

Probability = 0.0401

(d)

P(x < 216) = P[(x - ) / < (216 - 252) / 16]

= P(z < -2.25)

= 0.0122

baby's are unusual because probability < 0.05