Statistics and Probability Answers

A survey finds the following probability distribution for the age of a rented car:
Age in years 0 – 1 1 – 2 2 – 3 3 – 4 4 – 5 5 – 6 6 – 7
Probability 0.10 0.26 0.28 0.20 0.11 0.04 0.01
a. Find the probability that a rented car is between 0 and 4 years old.
b. Find the mean
Find the variance

1 Determine the probability of a sum of 11 or 9 appears in a single toss of a pair of fair dice
2 At least one tail appears in two tosses of a fair coin
3 In an experiment a coin is tossed 4 times.Find the probability of getting at least 2 heads and 1tail.

Direct Materials: 24kg @ $3.00 $ 72.00
Direct Labour: 6 hours @ $6.50 39.00
Factory overhead: 6 hours @ $0.75 4.50
Total unit standard cost $ 115.50
The factory overhead was based on the following flexible budget, in which 90% is normal capacity.
80% 90% 100%
Hours (direct labour) 40,000 45,000 50,000
Variable expenses $20,000 $22,500 $25,000



Actual data for November:

Fixed Expenses 11,250 11,250 11,250
Total Factory Overheads 31,250 33,750 36,250

Planned production, 7,500 units
Material put into production 192410kg @ $ 3.04 (average cost) Direct Labour 46,830 hours @ $6.60 average labour cost Actual FOH $ 36,340
Other data:
Beginning inventory, work in process, 80 units, all material, 50% converted Ending inventory, work in process, 100 units, all material, 50% converted Started in process during November 7,850 units

Required:
A variance analysis of
Material (Overall, Price and Usage)
FOH (Overall, Spending and Capacity)

Researchers studying people’s sense of smell devised a measure of smelling ability. A higher score on this scale means the subject can smell better. A random sample of 36 people (18 male and 18 female) were involved in the study. The average score for the males was 10 with a standard deviation of 3.4 and the average score for the females was 11 with a standard deviation of 2.7. Which of the following is the correct standard error for the test evaluating whether the males and females have differing smelling abilities, on average? Choose the closest answer.