Question

The lengths of a particular​ animal's pregnancies are approximately normally​ distributed, with mean μ=261 days and standard deviation σ=20 days.

​(a) What proportion of pregnancies lasts more than 296 ​days?

​(b) What proportion of pregnancies lasts between 256 and 266 ​days?

​(c) What is the probability that a randomly selected pregnancy lasts no more than 251 ​days?

​(d) A​ "very preterm" baby is one whose gestation period is less than 231 days. Are very preterm babies​ unusual?

Answer 1

μ=261 days

σ=20 days

Z= (Xbar-mu)/(sd) is the formula for normal distribution

a)Z=(296-261)/20 =1.75

P(Z>1.75) =0.04 (From Z curve find area under the curve for z value more than 1.75)

Hence we can say that 4% is the proportion of pregnancies lasts more than 296 ​days

b) Z=(256-261)/20 = -0.25

& Z=(266-261)/20 = 0.25

P(Z>-0.25 & Z<0.25) =19.74%

c) The probability that a randomly selected pregnancy lasts no more than 251 ​days

Z=(251-261)/20 = -0.5

P(Z>-0.5)=69.15%

d) = (231-261)/20 = -1.5

P(Z<-1.5)=6.68%

Hence we can say that the probability of premature babies are 6% which is not very unusual.

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