Question

The length of human pregnancies from conception to birth varies according to a distribution that can be modeled by a normal random variable with mean 269 days and standard deviation 18 days

QUESTION 1: What percent of pregnancies last less than 240 days? Note that the answer is requested as a percent. Use 2 decimal places in your answer

QUESTION 2: What percent of pregnancies last between 240 and 270 days? Note that the answer is requested as a percent. Use 2 decimal places in your answer

QUESTION 3: The longest 20% of pregnancies last at least how many days? (round to the nearest whole day)

Answer 1

This is a normal distribution question with

a) x = 240

P(x < 240.0)=?

The z-score at x = 240.0 is,

z = -1.6111

This implies that

P(x < 240.0) = P(z < -1.6111) = 0.0536

b) x1 = 240

x2 = 270

P(240.0 < x < 270.0)=?

c) Given in the question

P(X>x)=0.20 is

P(X < x) = 0.8

This implies that

P(Z < 0.8416) = 0.8

With the help of formula for z, we can say that

x = 284.15

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

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