Answer:
a) 0.04
b) 0.54674
c) 0.10565
d) It is not unusual to have preterm babies
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