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.

Step-by-step 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 : $z=\dfrac{x-\mu}{\sigma}$

$1.28155=\dfrac{x-26}{4}\\\\ x-26=4\times1.28155\\\\ x-26=5.1262\\\\ x=5.1262+26=31.1262\approx31.13$

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