Question

Chapter 3 Basic Statistics: A Review 11. Suppose that the weight W of male patients registered of male patients registered at a diet clinic has the normal e weight distribution with mean 190 and variance 100 a. For a random sample of patients of size n 25, the expression PW 180). in which W denotes the sample mean weight, is equivalent to saying1 [Note: Z is a standard normal random variable.] b. Find an interval (a, b) such that Pa W<b)80 for the same random sam- ple in part (a).

Answer 1

a)

here as we know that z score =(Wbar-mean)*sqrt(n/Variance)

hence P(Wbar <180) =P(Z<(180-190)*sqrt(25/100))=P(Z<-5) =P(Z>5)

therefore required value is 5

b)

for 80% middle values ; critical z =1.28

therefore a =mean-z*sqrt(variance/n) =190-1.28*sqrt(100/25)=190-2.56=187.44

b=a =mean+z*sqrt(variance/n) =190+1.28*sqrt(100/25)=190+2.56=192.56