Question

(1 point)

The length of human pregnancies from conception to birth varies according to a distribution that is approximately Normal with mean 266 days and standard deviation 16 days.

A. Find the probability that the average pregnancy length for 7 randomly chosen women exceeds 270 days. (Use at least five decimals of accuracy in your answer)

Probability =

B. Find the probability that the average pregnancy length for 27 randomly chosen women exceeds 270 days. (Use at least five decimals of accuracy in your answer)

Probability =

Answer 1

A)

for normal distribution z score =(X-μ)/σx
here mean=       μ=	266
std deviation   =σ=	16.000
sample size       =n=	7
std error=σx̅=σ/√n=	6.047

probability that the average pregnancy length for 7 randomly chosen women exceeds 270 days.:

probability =P(X>270)=P(Z>(270-266)/6.047)=P(Z>0.66)=1-P(Z<0.66)=1-0.7454=0.2546

B)

sample size       =n=	27
std error=σx̅=σ/√n=	3.07920

Probability that the average pregnancy length for 27 randomly chosen women exceeds 270 days :

probability =P(X>270)=P(Z>(270-266)/3.079)=P(Z>1.3)=1-P(Z<1.3)=1-0.9032=0.0968