Question

1. (Use Table V for this problem.) The length of human pregnancies varies according to a distribution which is approximately normal with mean 266 days and standard deviation 16 days.

(a) What percent of pregnancies last less than 240 days (about 8 months)?

(b) What percent of pregnancies last more than 270 days (about 9 months)?

(c) What percent of pregnancies last between 240 days and 270 days (about 8 to 9 months)?

(d) What is the cutoff separating the longest 20% of the pregnancies from the other 80%?

(e) What is the cutoff separating the shortest 30% of the pregnancies from the other 70%?

(f) What interval contains the middle 90% of pregnancy lengths?

Answer 1

This is a normal distribution question with


a) P(x < 240.0)=?
The z-score at x = 240.0 is,

z = -1.625
This implies that


b) P(x > 270.0)=?
The z-score at x = 270.0 is,

z = 0.25
This implies that
P(x > 270.0) = P(z > 0.25) = 1 - 0.5987063256829237


c) P(240.0 < x < 270.0)=?

This implies that
P(240.0 < x < 270.0) = P(-1.625 < z < 0.25) = P(Z < 0.25) - P(Z < -1.625)
P(240.0 < x < 270.0) = 0.5987063256829237 - 0.05208127941521953


d) Given in the question
P(X > x) = 0.2
This implies that
P(Z > 0.8416) = 0.2
With the help of formula for z, we can say that

x = 279.4656

e) Given in the question
P(X < x) = 0.3
This implies that
P(Z < -0.5244) = 0.3
With the help of formula for z, we can say that

x = 257.6096

f) Given in the question
P(X < x) = 0.05
This implies that
P(Z < -1.6449) = 0.05
With the help of formula for z, we can say that

x = 239.6816

Given in the question
P(X < x) = 0.95
This implies that
P(Z < 1.6449) = 0.95
With the help of formula for z, we can say that

x = 292.3184
PS: you have to refer z score table to find the final probabilities.
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