Question

Assume the duration of human pregnancies can be described by a Normal model with mean 266 days and standard deviation 16 days. 1. What percentage of pregnancies should last between 270 and 280 days? 2. At least how many days should be the longest 25% of all pregnancies last? 3. Suppose a certain obstetrician is providing prenatal care to 60 pregnant women. According to the Central Limit Theorem, if we calculated sample means, what is the mean and standard deviation of the distributions of these sample means? 4. What is the probability that the mean duration of these patients’ pregnancies will be less than 260 days?

Answer 1

Mean = = 266

Standard deviation = = 16

1)

We have to find P( 270 < X < 280)

For finding this probability we have to find z score.

That is we have to find P( 0.25 < Z < 0.88)

P( 0.25 < Z < 0.88) = P(Z < 0.88) - P(Z < 0.25) = 0.8092 - 0.5987 = 0.2105

( From z table)

Percent = 21.05%

2)

We have given P(X > x) = 0.25

z value 0.25 is 0.67

We have to find value of x

3)

Mean = = 266

Standard deviation is

4) Sample size = n = 60

We have to find P( < 260)

For finding this probability we have to find z score.

That is we have to find P(Z < - 2.90)

P(Z < - 2.90) = 0.0018

( From z table)

The probability that the mean duration of these patients’ pregnancies will be less than 260 days is 0.0018