In the United States, the mean age of men when they marry for the first time follows the normal distribution with a mean of 24.6 years. The standard deviation of the distribution is 2.8 years. For a random sample of 66 men, what is the likelihood that the age when they were first married is less than 25 years?

So we want to find this probability:

And using the normal standard distirbution or excel we got:

Step-by-step explanation:

Let X the random variable that represent the age of men married of a population, and for this case we know the distribution for X is given by:

Where and

We are interested on this probability

The sample size is n =66. We can use the z score to solve this problem:

If we find the z score for 25 we got:

So we want to find this probability:

And using the normal standard distirbution or excel we got:

98%

step-by-step explanation: