Discuss the below:
Q: A samples contains 1,000 values. The histogram for this sample is bell-shaped. Approximately 950 values in the sample are known to be within $100 of the mean. Suppose the mean is $5,000. Use Empirical Rule to perform the following:
a. Calculate a value for the standard deviation.
b. determine the data value that is 97.5 percentile
c. Calculate the z-score for 116th percentile
The division manager for Northern Pipe and Steel Company decided to implement a new intensive system for the managers of Northern's three plants. The plan called for a bonus to be paid the next month to the manager whose plant had the greatest relative improvement over the average monthly production volume. The following data reflected the historical production volumes at the three plants.
Plant1: m=700, q=200
Plant2: m=2300, q=350
Plant3: m=1200, q=30
At the close of the next month.the monthly output for the three plants was
Plant1 810
Plant2 2600
Plant3 1320
Suppose the division manager awarded the bonus to the manager of Plant2 because her plant increased by over units over the mean. What was a bigger increase that that of any of the other managers. Do you agree with who received the bonus this month? Explain, using the appropriate statistical measures to support your position.