Question

Conslder a largo population or interest its distributIon Is normal and t's mean 185 and standard deviatlon is 1 10. Let X-a alnglC 0030~atlon Round al probabilties to four decimals) a) Find PO190 b) Find FiX 190 Conelder anothr large populaton o interest ITs distntution is unknoun and it's mean Is 185 and tstandand davaton is 110. Let-a snale observaton

Answer 1

a)

for normal distribution z score =(X-μ)/σ
here mean=       μ=	185
std deviation   =σ=	110.0000

probability =

P(X<190)

=

P(Z<0.05)=

0.5199

b)

sample size       =n=	130
std error=σx̅=σ/√n=	9.6476

probability =

P(Xbar<190)

=

P(Z<0.52)=

0.6985

c)

as sample size is greater then 30 therefore sample mean can be apprximated as normally distributed

hence

probability =

P(Ybar<190)

=

P(Z<0.52)=

0.6985