Question

The lengths of pregnancies in a small rural village are normally distributed with a mean of 270 days and a standard deviation of 16 days. In what range would you expect to find the middle 95% of most pregnancies? Between and . If you were to draw samples of size 43 from this population, in what range would you expect to find the middle 95% of most averages for the lengths of pregnancies in the sample? Between and . Enter your answers as numbers. Your answers should be accurate to 1 decimal places.

Answer 1

1)

mean μ=	270
standard deviation σ=	16.0000

for middle 95% values , critical z = -/+ 1.96

therefore corresponding middle 95% of most pregnancies =mean -/+ z*std deviation

=270 -/+ 1.96*16 = between 238.6 and 301.4

2)

for sample size n=43 :

sample size       =n=	43
std error=σx̅=σ/√n=	2.4400

corresponding middle 95% of most pregnancies =mean -/+ z*std deviation

=270 -/+ 1.96*2.44 = between 265.2 and 274.8