5.3 The manager of a large computer network has developed
the following probability distribution of the number of
interruptions per day:
Interruptions (X) P1X2
0 0.32
1 0.35
2 0.18
3 0.08
4 0.04
5 0.02
6 0.01
a. Compute the expected number of interruptions per day.
b. Compute the standard deviation.
Need step by step directions to do this in 2010 Excel spreadsheet.
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To compute the expected number of interruptions per day and the standard deviation using Excel, you can follow these step-by-step directions:
a. Computing the Expected Number of Interruptions per Day:
Step 1: Open a new Excel spreadsheet.
Step 2: Create a table with two columns. In column A, label the first cell as "Interruptions (X)" and list the values 0 to 6 in the subsequent cells. In column B, label the first cell as "P(X)" and enter the corresponding probabilities provided in your question (0.32, 0.35, 0.18, 0.08, 0.04, 0.02, 0.01) in the subsequent cells.
Step 3: In an empty cell, type "=SUMPRODUCT(A2:A8, B2:B8)" to calculate the expected number of interruptions per day. This formula multiplies each value of "X" with its corresponding probability and then sums them up. Press Enter to get the result, which should be 1.85.
b. Computing the Standard Deviation:
Step 4: In a new column, label the first cell as "X*P(X)". In the subsequent cells below this label, multiply the values in the "Interruptions (X)" column (column A) with their corresponding probabilities in the "P(X)" column (column B) using the formula "=A2*B2". Drag the formula down to fill all the cells in this column.
Step 5: In an empty cell, type "=SUMPRODUCT((A2:A8-E3)^2, B2:B8)" to calculate the variance. This formula subtracts each value of "X" in column A with the expected value obtained in step 3, squares the differences, multiplies them by their corresponding probabilities, and finally sums them up. Press Enter to get the result.
Step 6: In another empty cell, type "=SQRT(D3)" to calculate the standard deviation. This formula takes the square root of the variance calculated in step 5.
By following these steps, you will obtain the expected number of interruptions per day and the standard deviation using an Excel spreadsheet based on the given probability distribution.