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?

Answer:

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

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