Question

6) For these you will need to calculate the z-score then find the area. Assume that the height of men is a normally distributed variable with a m = 69.0” and s = 3.0”

a) What is the probability that a randomly selected man is taller than 72.0”?

b) What proportion of men are taller than 65.0”?

c) What proportion of men are between 67.0” and 71.0” tall?

Answer 1

a)

for normal distribution z score =(X-μ)/σx
here mean=       μ=	69
std deviation   =σ=	3.0000

probability that a randomly selected man is taller than 72.0” :

probability =

P(X>72)

=

P(Z>1)=

1-P(Z<1)=

1-0.8413=

0.1587

b)

proportion of men are taller than 65.0 :

probability =

P(X>65)

=

P(Z>-1.333)=

1-P(Z<-1.33)=

1-0.0918=

0.9082

c)

probability =

P(67<X<71)

=

P(-0.67<Z<0.67)=

0.7486-0.2514=

0.4972