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 ([tex]\mu[/tex]) 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 ([tex]\sigma[/tex]) 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 : [tex]z=\dfrac{x-\mu}{\sigma}[/tex]
[tex]1.28155=\dfrac{x-26}{4}\\\\ x-26=4\times1.28155\\\\ x-26=5.1262\\\\ x=5.1262+26=31.1262\approx31.13[/tex]
Hence, 90% of people getting married for the first time get married before age of 31.13.
