Question

4.The average age for a person getting married for the first time is 26 years (U.S. News and World Report, June 6, 1994). Assume the ages for first marriages have a normal distribution with a standard deviation of four years.

a)What is the probability that a person getting married for the first time is younger than 23 years of age?

b)What is the probability that a person getting married for the first time is in his or her twenties?

c)90% of people getting married for the first time get married before what age?

Answer 1

(a)

=26

= 4

To find P(X<23):

Z = (23 - 26)/4

= - 0.75

By Technology, Cumulative Area Under Standard Normal Curve = 0.2266

So,

Answer is:

0.2266

(b)

Tofind P(X =20) = 0, because the probability at a particular value of X = 0 in the case of a continuous distribution.

So,

Answer is:
0.0000

(c)

90% of people correspond to area = 0.90 - 0.50 = 0.40.from mid value to RHS.

Table of Area Under Standard Normal Curve gives Z = 1.28.

So,

we get:
Z = 1.28 = (X - 26)/4

So,

X = 26 + (1.28 X 4)

= 31.12

So,

Answer is:

31.12