The mean age at which men in the United States marry for the first time follows the normal distribution with a mean of 24.1 years. The standard deviation of the

Question

The mean age at which men in the United States marry for the first time follows the normal distribution with a mean of 24.1 years. The standard deviation of the distribution is 2.5 years.

For a random sample of 66 men, what is the likelihood that the age at which they were married for the first time is less than 24.6 years? (Round z value to 2 decimal places. Round your answer to 4 decimal places.)

Answer 1

Ok, we're given the population mean mu (24.1) and the population sd sigma (2.5), and we know the population is normally distributed. Per the Central Limit Theorem we know that samples of size n will have

sample means x-bar = mu, and sample standard deviations s = sigma/sqrt(n).

 

Therefore, z = (24.6 - 24.1)/(2.5/sqrt(66)) = 1.62. From a standard normal table, z = 1.62 equates to a left-tail area of 

.9474. Thus, 94.74% of samples of size n=66 taken from this distribution will have sample means of 24.6 or less.

 

Note: z-score for a sample is:     z =  (x-bar - mu)/(sigma/sqrt(n))