Question

A sample of size 36 cases is drawn from a negatively skewed population with mean of 2 and standard deviation of 3. what is the probability that the sample mean obtained will be negative? How many points must we go from the mean to include 50 percent of all sample means.

Answer 1

here as sample size is greater than 30 ; from central limit therum we can apply normal approximation:

a)

here mean=       μ=	2
std deviation   =σ=	3.000
sample size       =n=	36
std error=σx̅=σ/√n=	0.5000

a)  probability that the sample mean obtained will be negative :

P{X<0)=P(Z<(0-2)/0.5)=P(Z<-4)=0.000032

b)

for middle 50% values fall between 25 and 75 th percentile for whcih critical z =-/+0.67

hence corresponding points =z*std error =0.67*0.5=0.34 points on both sides of mean