Assume that the duration of human pregnancies can be described by a Normal model

Question

Assume that the duration of human pregnancies can be described by a Normal model with mean 264 days and standard deviation 14 days.

a) What percentage of pregnancies should last between 268 and 278 days?

b) At least how many days should the longest 30% of all pregnancies last?

c) Suppose a certain obstetrician is currently providing prenatal care to 55 pregnant women. Let y represent the mean length of their pregnancies. According to the Central Limit Theorem, what's the distribution of this sample mean, y ? Specify the model, mean, and standard deviation.

d) What's the probability that the mean duration of these patients' pregnancies will be less than 260 days?

Explanation / Answer

Ans:

Given that

mean=264

standard deviation=14

a)

z(268)=(268-264)/14=0.286

z(278)=(278-264)/14=1

P(0.286<z<1)=P(z<1)-P(z<0.286)=0.8413-0.6125=0.2289

b)

P(Z>=z)=0.3

z=normsinv(0.7)=0.5244

x=264+0.5244*14=271.34 days

c)sampling distribution of sample means:

mean=264

standard deviation=14/sqrt(55)=1.89

d)

z=(260-264)/1.89=-2.12

P(z<-2.12)=0.0170

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