a frequency distribution is shown below. the number of overtime hours worked in

Question

a frequency distribution is shown below. the number of overtime hours worked in one week peremployee overtime hours 0 1 2   3   4   5  6 employees        6 15 30 5443 32 13 use the frequency distribution to construct a probabilitydistribution x      p(x) 0 1 2 3 4 5 6 bb) find the mean of the probability distribution c) find the variance of the probability distribution d) find the standard deviation of the probabilitydistribution a frequency distribution is shown below. the number of overtime hours worked in one week peremployee overtime hours 0 1 2   3   4   5  6 employees        6 15 30 5443 32 13 use the frequency distribution to construct a probabilitydistribution x      p(x) 0 1 2 3 4 5 6 bb) find the mean of the probability distribution c) find the variance of the probability distribution d) find the standard deviation of the probabilitydistribution

Explanation / Answer

x      p(x) 0      6/193=0.031
1      15/193=0.078
2      30/193=0.155
3      54/193=0.28
4      43/193=0.223
5      32/193=0.166
6      13/193=0.067


b) find the mean of the probability distribution
E(X)=0*0.031 +1*0.078 +2*0.155 +3*0.28 + 4*0.223 + 5*0.166 +6*0.067=3.352

c) find the variance of the probability distribution
E(X^2)=0*0.031 +1^2*0.078 +2^2*0.155 +3^2*0.28 + 4^2*0.223 +5^2*0.166 +6^2*0.067=13.348
Var(X)=E(X^2)-[E(X)]^2 = 13.348-3.352^2=2.112

d) find the standard deviation of the probabilitydistribution

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