Question

A sample of final exam score is normally distributed with a mean equal to 20 and a variance equal to 25

(a) what percentage of scores is between 15 and 25

(b) what raw score is the cutoff for the top 10% of scores

(c) what is the probability of a score less then 27

(d) what is proportion below 13

Answer 1

for normal distribution z score =(X-μ)/σx
here mean=       μ=	20
std deviation   =σ=	5

a)

probability =

P(15<X<25)

=

P(-1<Z<1)=

0.8413-0.1587=

0.6826

b)

for top 10th percentage values are at 90th percentile:

for 90th percentile critical value of z=		1.28
therefore corresponding value=mean+z*std deviation=			26.40

c)

probability =

P(X<27)

=

P(Z<1.4)=

0.9192

d)

probability =

P(X<13)

=

P(Z<-1.4)=

0.0808