In the United States, the mean age of men when they marry for the first time follows the normal distribution with a mean of 24.7 years. The standard deviation of the distribution is 2.8 years. For a random sample of 60 men, what is the likelihood that the age when they were first married is less than 25.2 years

The likelihood is

Step-by-step explanation:

From the question we are told that

     The population mean is  

      The standard deviation is  

      The sample size is

       The  consider random value is  x =  25.2  years

Given that mean age is normally distributed, the likelihood that the age when they were first married is less than x is mathematically represented as

Generally  

So

Where is the standard error of the sample mean which mathematically evaluated as

substituting values

So  

From z-table the value for  P(Z<    1.3831  ) is

  So

add an image

step-by-step explanation: