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

P(X < A) = P(Z < (A - mean)/standard deviation)

Mean = 26 years

Standard deviation = 4 years

a) P(X < 23) = P(Z < (23 - 26)/4)

= P(Z < -0.75)

= 0.2266

b) P(20 < X < 30) = P(Z < 30) - P(Z < 20)

= P(Z < (30 - 26)/4) - P(Z < (20 - 26)/4)

= P(Z < 1) - P(Z < -1.5)

= 0.8413 - 0.0668

= 0.7745

c) Let 90% people get married for the first time by M

P(X < M) = 0.90

P(Z < (M - 26)/4) = 0.90

Take the value of z corresponding to 0.90 from standard normal distribution table.

(M - 26)/4 = 1.28

M = 31.12 years