# Written Midterm Review 2 2

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SOC 2061: midterm review Name:
_______________________________
Please be sure to show all your work on this exam, including any
formulas used, calculations conducted, and drawings used to arrive at
1. The mean age at first marriage for respondents in a survey is 23.33, with
a standard deviation of 6.13
a. Calculate the Z score associated with an observed age at first marriage
of 25.50 and explain what the Z score tells you.
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

b. Calculate the observed age at first marriage associated with a Z score
of -0.72.
Given ,z-score of -0.72
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
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c. What proportion of respondents were married for the first time between
the ages of 20 and 30?
P(20<X<30) = P( 
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  
d. If an individual was married for the first time at the age of 35, what
percentile is he or she in?

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SOC 2061: midterm review Name:
_______________________________
Please be sure to show all your work on this exam, including any
formulas used, calculations conducted, and drawings used to arrive at
P(X<35)=  
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
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2. In a normal distribution, how many standard deviations from the mean is
the 95
th
percentile?
In a normal distribution the mean is 95
th
percentile by 1.96 standard
deviation.
Here, percentile is 95%
Z-score corresponding to 95
th
percentile is 1.96
Using Excel formula, =NORM.S.INV(0.975)
3. According to the central limit theorem what happens to the sampling
distribution of sample means as N becomes larger?
According to central limit theorem.the distribution becomes normal when as N
becomes larger.The sampling distribution would become more smoother and bell
shaped.
4. The Law School Admission Test (LSAT) is designed so that test scores are
normally distributed. The mean LSAT score for the population of all test-
takers in 2005 was 154.35 with a standard deviation of 5.62.
a. What is the mean of the sampling distribution for samples of size 100?
The mean of the sampling distribution of size 100 will be the mean LSAT
score of all test-takes which is 154.34.
b. What is the standard error of the sampling distribution for samples of
size 100?

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SOC 2061: midterm review Name: _______________________________ Please be sure to show all your work on this exam, including any formulas used, calculations conducted, and drawings used to arrive at your answers! 1. The mean age at first marriage for respondents in a survey is 23.33, with a standard deviation of 6.13 a. Calculate the Z score associated with an observed age at first marriage of 25.50 and explain what the Z score tells you. Answer 𝑧 − 𝑠𝑐𝑜𝑟𝑒 = 𝑋−𝑀𝑒𝑎𝑛 𝑠𝑑 = 25.5−23.33 6.13 = 0.3540 b. Calculate the observed age at first marriage associated with a Z score of -0.72. Answer Given ,z-score of -0.72 −0.72 = 𝑋−23.33 6.13 => 𝑋 = 18.92 c. What proportion of respondents were married for the first time between the ages of 20 and 30? Answer P(20 ...
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