Question

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

Answer 1

Answer: 90% of people getting married for the first time get married before age of 31.13.

Explanation:

Given : The average age (
`\mu`) for a person getting married for the first time is 26 years (U.S. News and World Report, June 6, 1994).

We assume that the ages for first marriages have a normal distribution with a standard deviation (
`\sigma`) of 4 years.

Let x be the age before that 90% of people getting married for the first time get married.

From z-table , the value corresponds to p-value of 0.90 is 1.28155.

Formula :
`z=(x-\mu)/(\sigma)`

`1.28155=(x-26)/(4)\\\\ x-26=4*1.28155\\\\ x-26=5.1262\\\\ x=5.1262+26=31.1262\approx31.13`

Hence, 90% of people getting married for the first time get married before age of 31.13.