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Constructing a probability distribution using a frequency distribution

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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.

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Solution Summary

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

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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 ...

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