Question

Assume that the duration of human pregnancies can be described by a Normal model with mean 267 days and standard deviation 18 days.​

a) What percentage of pregnancies should last between 270 and 277 days?​

b) At least how many days should the longest 15​% of all pregnancies​ last?​

c) Suppose a certain obstetrician is currently providing prenatal care to 71 pregnant women. Let y overbar represent the mean length of their pregnancies. According to the Central Limit​ Theorem, what's the distribution of this sample​ mean, y overbar​? 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?

a) The percentage of pregnancies that should last between 270 and 277 days is ___%. (Round to two decimal places as needed.)

b) The longest 15% of all pregnancies should last at least ___% days. (Round to one decimal places as needed.)

c) Select the correct choice below and, if necessary, fill in the answer box(es) within your choice.

A. A Normal model with mean ___ and standard deviation ___. (Type integers or decimals rounded to two decimal places as needed.)

B. A Binomial model with ___ trials and a probability of success of ___. (Type integers or decimals rounded to two decimal places as needed.)

C. There is no model that fits this distributioin.

d) The probability that the mean duration of these patients' pregnancies will be less than 250 days is ___. (Round to four decimal places as needed.)

Answer 1

a)

probability =P(270<X<277)=P((270-267)/18)<Z<(277-267)/18)=P(0.17<Z<0.56)=0.7123-0.5675=0.1448~ 14.48%

b)

for 85th percentile critical value of z=		1.04
therefore corresponding value=mean+z*std deviation=			269.2 days

c)

std error=σx̅=σ/√n=

2.1362

. A Normal model with mean 267   and standard deviation 2.14

d)

probability =P(X<250)=(Z<(250-267)/2.136)=P(Z<-7.96)=0.0000