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 12 days. Answer the following questions. the foillwing queatinsby normal a) What percentage of pregnancies should last between 275 and 285 days? % (Round to one decimal place as needed.) b) At least how many days should the longest 20% of all pregnancies last? P(X2 D=0.20 (Round to one decimal place as needed.) c) Suppose a certain obstetrician is currently providing prenatal care to 70 pregnant women. Let y represent the mearn 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 SD(y)- (Round to two decimal places as needed.) d) What is the probability that the mean duration of these patients' pregnancies will be less than 261 days? P(y

Explanation / Answer

mean is 264 and s is 12

a) z is given as (x-mean)/s thus P(275<x<285)=P((275-264)/12<z<(285-264)/12)=P(0.92<z<1.75) or P(z<1.75)-P(z<0.92), from normal distribution table we get 0.9599-0.8212=0.1387

b) we need the z value from left of curve for 1-0.2 i.e 80% which is 0.85

thus answer is mean+z*SE=264+12*0.85=274.2

c) for sample size of 70

the mean is same 264 and

standard error is SE=s/sqrt(N)=12/sqrt(70)=1.4346

d) P(x<261)=P(z<(261-264)/1.4346)=P(z<-2.09) or 1-P(z<2.09)

from normal distribution table we get 1-0.9817=0.0183

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.