Question

The ASVAB scores for Marines joining the Marine Corps are normally distributed with mean 75 and standard deviation 10.

a) State what the random variable represents in this problem (i.e. Let random variable X denote….).

b) What are the parameters needed to use this distribution, and what are the values (i.e. mu = …)?

c) What fraction of the scores are between 80 and 90? Write a probability statement and solve (you can use Excel).

d) What is the 90th percentile of this distribution?

Answer 1

a) random variable X denote ASVAB score of a randomely selected Marine joining the Marine Corps

b)

below are parameter for scores:

=75

and =10

c)

probability =

P(80<X<90)

=

P(0.5<Z<1.5)=

0.9332-0.6915=

0.2417

(we have used excel function :norm.dist(90,75,10,true)-norm.dist(80,75,10,true))

d)

for 90th percentile critical value of z=		1.28
therefore corresponding value=mean+z*std deviation=			87.8