Question

A normal distribution of scores in population has a mean of µ = 100 with σ = 20. A. What is the probability of randomly selecting a score greater than X = 110 from this population? B. If a sample of n = 25 scores is randomly selected from this population, what is the probability that the sample mean will be greater than M = 110?

Answer 1

a)

for normal distribution z score =(X-μ)/σ
here mean=       μ=	100
std deviation   =σ=	20.0000

probability of randomly selecting a score greater than X = 110 from this population:

probability =

P(X>110)

=

P(Z>0.5)=

1-P(Z<0.5)=

1-0.6915=

0.3085

B)

sample size       =n=	25
std error=σx̅=σ/√n=	4.0000

probability that the sample mean will be greater than M = 110:

probability =

P(X>110)

=

P(Z>2.5)=

1-P(Z<2.5)=

1-0.9938=

0.0062