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 269 days and standard deviation 16 days. Answer the following questions. a) What percentage of pregnancies should last between 270 and 285 days? (Round to one decimal place as needed.) b) At least how many days should the longest 20% of all pregnancies last? PlX2D. 0.20 (Round to one decimal place as needed.) c) Suppose a certain obstetrician is currently providing prenatal care to 30 pregnant women. Let y represent the mean length of their pregnancies. According to the central limit theorem, what is the mean and standard deviation SD(y) of the normal model of the distribution of the sample mean, y? The mean is soy). (Round to two decimal places as needed.) d) What is the probability that the mean duration of these patients' pregnancies will be less than 268 days? Ply

Explanation / Answer

Ans:

mean=269 and std dev=16

a)

z(270)=(270-269)/16=0.0625

z(285)=(285-269)/16=1

P(0.0625<z<1)=P(z<1)-P(z<0.0625)=0.8413-0.5249=0.3164

31.6%

b)P(Z>=z)=0.2

P(Z<z)=1-0.2=0.8

z=0.8416

x=269+0.8416*16=282.5

c)

mean=269

std dev=16/sqrt(30)=2.92

d)

z(268)=(268-269)*sqrt(30)/16=-0.342

P(z<-0.342)=0.366

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