Discuss the folloiwng:
1. The distribution of the grades in the class of Statistics is shown below:
a) Calculate a cumulative frequency distribution, and a cumulative relative frequency distribution that will be shown in two columns in your table above.
b) Using Excel, draw a histogram of the frequencies and paste it in the space provided below.
c) On the basis of the shape of the histogram, make an assessment about symmetry in the data, its probable cause, and the implication for the mean of the group.
d) Using the appropriate formula for grouped data, calculate the mean score of this class. Use the table provided above for your computations.
e) Using the appropriate formulas for grouped data, calculate the variance and the standard deviation. Use the table provided above for your computations.
2. A company specializes in installing and servicing central heating furnaces. In a pre-winter period, service calls may result in an order for a new furnace. The table shows estimated probabilities for numbers of new furnace orders generated in this way in the last two weeks of September.
[The calculations and the graph for this exercise must be made on Excel from where you will cut your findings and paste them in the appropriate places.]
Number of orders 0 1 2 3 4 5
Probabilities 0.10 0.14 0.26 0.28 0.15 0.07
a. Graph the probability distribution.
b. Calculate and draw the cumulative probability function.
c. Find the probability that at least three orders will be generated this period.
d. Find the mean of the number of orders for new furnaces in this period of two weeks.
e. Find the standard deviation of the number of orders for new furnaces in this period of two weeks and give the range of orders that could
be realized with approximately 68% of probability.