Question

The average age for a person getting married for the first time is 26 years.

Assume that the ages for the first marriages have a normal distribution with a standard deviation of about 4 years.90% of people getting married for the first time get married before what age?

Answer 1

90% of people getting married for the first time get married before 32 years.

Explanation:

The average age for a person getting married for the first time is 26 years i.e.
`\mu=26`

The ages for the first marriages have a normal distribution with a standard deviation of about 4 years i.e.
`\sigma = 4`

90% of people getting married for the first time.

The z-value at 90% confidence interval is z=1.64.

The z-score formula is given by,

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

Where, x is the required sample mean or age.

Substitute the values,

`1.64=(x-26)/(4)`

`1.64* 4=x-26`

`6.56=x-26`

`x=6.56+26`

`x=32.56`

Therefore, 90% of people getting married for the first time get married before 32 years.