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In the United States, the mean age of men when they marry for the first time follows the normal distribution with a mean of 29 years. The standard deviation of the distribution is 2.5 years. For a random sample of 60 men, what is the likelihood that the age when they were first married is less than 29.3. years?

Respuesta :

Answer:

Step-by-step explanation:

Let X represent the age of men when they marry for the first time  in the United States.

Given x bar follows normal with mean = 29 years and sigma = 2.5 years

Sample size =n= 60 men

Std error of sample = [tex]\frac{\sigma}{\sqrt{n} } =\frac{2.5}{\sqrt{60} } \\=0.3227[/tex]

The  likelihood that the age when they were first married is less than 29.3. years

[tex]=P(X bar <29.3)=P(Z<\frac{29.3-29}{0.3227} \\=P(Z<0.93)[/tex]

=0.8238

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