The table to the right gives data on a survey of the number of times married for

Question

The table to the right gives data on a survey of the number of times married for men of age 20 to 24. For the observations, x bar = 0.20 and s = 0.42. Use this information to answer parts a and b. Find the actual percentages of observations within one, two, and three standard deviations of the mean. How do these compare to the percentages predicted by the Empirical Rule? 80.5% of the observations are within one standard deviation of the mean. 99.4% of the observations are within two standard deviations of the mean. % of the observations are within three standard deviations of the mean.

Explanation / Answer

by Empirical rule,

the observations within one sd of the mean= xbar +- s

=0.20+0.42 and 0.20-0.42

= -0.22,0.62

the observations between interval (-0.22,0.62)=6221

% calculation= (6221/7726)*100=80.50

80.5% of the observations are within one standard deviations of the mean.

b)

the observations within two sd of the mean= xbar +- 2s

=0.20+0.84 and 0.20-0.84

= -0.64,1.04

the observations between interval (-0.64,1.04)=6221+1458=7679

% calculation= (7679/7726)*100=99.391=99.4

99.4% of the observations are within two standard deviations of the mean.

c)

the observations within three sd of the mean= xbar +- 3s

=0.20+1.26 and 0.20-1.26

= -1.06,1.46

the observations between interval (-1.06,1.46)=6221+1458=7679

% calculation= (7679/7726)*100=99.391=99.4

99.4% of the observations are within three standard deviations of the mean.

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