SOLUTION: The mean age at which men in the United States marry for the first time follows the normal distribution with a mean of 24.7 years. The standard deviation of the distribution is 2.

Question 1037365: The mean age at which men in the United States marry for the first time follows the normal distribution with a mean of 24.7 years. The standard deviation of the distribution is 2.5 years. For a range sample of 55 men, what is the likelihood that the age at which they were married for the first time is less than 25 years? (round z value to 2 decimal places. Round your answer to 4 decimal places).
I finally figured out the first part, which is below:
25-24.7 = 0.3
Square root of 55 = 7.4161984
2.5 divided by 7.4161984 = 0.3370999
0.3 divided by 0.3370999 = 0.8899
I am not understanding how to do the second part to obtain the final answer. Can you please show me how you come up with the answer?
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
Let P stand for probability and X be the normal distribution variable
:
the problem asks us to calculate
:
P ( X < 25 )
:
since the sample size is > 30, we use the normal distribution and apply the Central Limit Theorem
:
the sample mean is taken to be the population mean
:
the sample standard deviation is taken to be population mean / square root of sample size
:
sample standard deviation = 2.5 / square root(55) = 0.337099931
:
the z-value is ( X - mean ) / sample standard deviation
:
z-value = ( 25 - 24.7 ) / 0.337099931 = 0.889943819 approx 0.89
:
now consult the table of z-values
:
*********************
P ( X < 25 ) = 0.8133
*********************
:

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