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Statistics and Probability

Amit has taken 3 tickets randomly from a pack of 10 lottery tickets in which 3 are winning

tickets and 7 are blanks. Somna has taken one ticket from a pack of 5 lottery tickets in which 2

are winnings and 3 blank tickets. Amongst Amit and Somna who has a better chance of winning

a prize.

Statistics and Probability

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

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

Statistics and Probability

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.

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.

Statistics and Probability

tickets and 7 are blanks. Somna has taken one ticket from a pack of 5 lottery tickets in which 2

are winnings and 3 blank tickets. Amongst Amit and Somna who has a better chance of winning

a prize.

Statistics and Probability

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)

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)

Statistics and Probability

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.

Statistics and Probability

We have two situations:

Assignment 10

All Together, Now

a) Pull 5 cards from a standard deck, replacing and shuffling each time, and count the number of face cards.

b) Deal five cards from a standard deck (without replacement). Count the number of face cards.

1. Create probability distributions for both of these situations. Include your tables. [4]

2. Calculate the expected number of face cards for each situation. [2]

3. Explain which probability distribution type you picked for each, and why. [2, Communication]

Assignment 10

All Together, Now

a) Pull 5 cards from a standard deck, replacing and shuffling each time, and count the number of face cards.

b) Deal five cards from a standard deck (without replacement). Count the number of face cards.

1. Create probability distributions for both of these situations. Include your tables. [4]

2. Calculate the expected number of face cards for each situation. [2]

3. Explain which probability distribution type you picked for each, and why. [2, Communication]

Statistics and Probability

The City of Hamilton forms a committee to improve low-income well-being in the city. A

committee of 5 people is to be formed from 11 ward councillors and 8 nonprofit representatives. If

they were picked at random...

1. Calculate the expected number of nonprofit representatives on this committee. [2]

2. Create a hypergeometric distribution graph, checking for number of nonprofit

representatives. Include the table with the graph. (To save yourself time, check back in the

lesson for the formulas to drop in your spreadsheet!) [3]

committee of 5 people is to be formed from 11 ward councillors and 8 nonprofit representatives. If

they were picked at random...

1. Calculate the expected number of nonprofit representatives on this committee. [2]

2. Create a hypergeometric distribution graph, checking for number of nonprofit

representatives. Include the table with the graph. (To save yourself time, check back in the

lesson for the formulas to drop in your spreadsheet!) [3]

Statistics and Probability

Pull 5 cards from a standard deck, replacing and shuffling each time, and count the number of face cards. Create probability distributions

Statistics and Probability

Out of 25 employees of a company, 5 are engineers. Three employees are selected at random for granting leave. What is the probability that (i) all the three are engineers?(ii) none of them is an engineer? (iii) at least one of them is an engineer?