The lengths of a particular animal's pregnancies are approximately normally distributed, with mean, μ = 272 days and standard deviation, σ = 16 days. (a) What proportion of pregnancies lasts more than 300 days? (b) What proportion of pregnancies lasts between 260 and 284 days? (c) What is the probability that a randomly selected pregnancy lasts no more than 252 days? (d) A "very preterm" baby is one whose gestation period is less than 236 days. Are very preterm babies unusual?

a) 0.04

b) 0.54674

c) 0.10565

d) It is not unusual to have preterm babies

Step-by-step explanation:

The lengths of a particular animal's pregnancies are approximately normally distributed, with mean, μ = 272 days and standard deviation, σ = 16 days.

We solve the above question using z score formula

z = (x-μ)/σ, where

x is the raw score

μ is the population mean

σ is the population standard deviation.

(a) What proportion of pregnancies lasts more than 300 days?

z = 300 - 272/16

= 1.75

Probability/proportion value from Z-Table:

P(x<300) = 0.95994

P(x>300) = 1 - P(x<300) = 0.040059

Approximately = 0.04

(b) What proportion of pregnancies lasts between 260 and 284 days?

For x = 260 days

z = 260 - 272/16

=-0.75

Probability value from Z-Table:

P(x = 260) = 0.22663

For x = 284

z= 284 - 272/16

=0.75

Probability value from Z-Table:

P(x = 284) = 0.77337

The proportion of pregnancies lasts between 260 and 284 days is

P(x= 284) - P(x = 260)

0.77337 - 0.22663

= 0.54674

(c) What is the probability that a randomly selected pregnancy lasts no more than 252 days?

No more than means less than or equal to, hence, we are to find

P ≤ 252 days

Hence,

z = 252 - 272/16

= -1.25

Probability value from Z-Table:

P(x ≤ 252) = 0.10565

(d) A "very preterm" baby is one whose gestation period is less than 236 days. Are very preterm babies unusual?

We find the probability of 236 days

For x = 236

z = 236 - 272/16

z = -2.25

Probability value from Z-Table:

P(x<236) = 0.012224

Converting to percentage = 1.2224%

Hence, it is not unusual to have preterm babies