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# Constructing a probability distribution using a frequency distribution

The table shows the number of overtime hours worked per week per employee. Use the frequency distribution to construct a probability distribution. Then find the mean, variance and standard deviation.

O/T 0 1 2 3 4 5 6 7
Empl 13 15 38 37 22 14 16 45

1) Mean
2) variance
3) standard deviation
Please explain in details step by step so I can understand what I am doing.
Thank you.

#### Solution Preview

In order to build the frequency distribution, we must first find the total number of observations. In order to do this, we sum all the frequencies from the table you gave:

Number of Observations = 13+15+38+37+22+14+16+45 = 200

Then, the probability of each outcome (each possible number of overtime hours) is calculated as:
(Frequency for that outcome)/(Number of Observations)

For example, there were 13 employees with 0 hours of overtime. So we conclude that the probability of an employee ...

#### Solution Summary

This solution provides the calculation of a probability distribution given a frequency distribution.

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