Question

A normal distribution has a mean of u = 54 and a

standard deviation of o = 6.

a. What is the probability of randomly selecting a

score less than X = 51?

b. What is the probability of selecting a sample of

n = 4 scores with a mean less than M = 51?

c. What is the probability of selecting a sample of

n = 36 scores with a mean less than M = 51?

Show your work

Answer 1

a)

for normal distribution z score =(X-μ)/σ
here mean=       μ=	54
std deviation   =σ=	6.000

probability of randomly selecting a score less than 51

probability =P(X<51)=(Z<(51-54)/6)=P(Z<-0.5)=0.3085

b)

sample size       =n=	4
std error=σx̅=σ/√n=	3.00

probability =P(X<51)=(Z<(51-54)/3)=P(Z<-1)=0.1587

c)

sample size       =n=	36
std error=σx̅=σ/√n=	1.00

probability =P(X<51)=(Z<(51-54)/1)=P(Z<-3)=0.0013