1. The mean age at first marriage for respondents in a survey is 23.33, with a s

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Question

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.

b. Calculate the observed age at first marriage associated with a Z score of -0.72.

c. What proportion of respondents were married for the first time between the ages of 20 and 30?

d. If an individual was married for the first time at the age of 35, what percentile is he or she in?

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.

Z=(25.50-23.33)/6.13 = 0.353996737

=0.35 ( two decimals)

This observed age at first marriage above 0.35 times standard deviation.

b. Calculate the observed age at first marriage associated with a Z score of -0.72.

x =23.33-0.72*6.13 = 18.9164

=18.92 ( two decimals)

c. What proportion of respondents were married for the first time between the ages of 20 and 30?

z value for 20, z =(20-23.33)/6.13 = -0.54

z value for 30, z =(30-23.33)/6.13 = 1.09

P( 20<x<30) = P( -0.54<z<1.09)

=P( z <1.09) – P( z <-0.54)

=0.8621 - 0.2946

=0.5675

d. If an individual was married for the first time at the age of 35, what percentile is he or she in?

z value for 35, z =(35-23.33)/6.13 = 1.90

percentile for z=1.90, p=0.9713 or 97.13%

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