Question

A sample of people were asked what was the usual way that they paid for alternative modes of public transportation Their responses are recorded in the following table:

	Taxi	Bus	Rail	Uber	TOTAL
Cash	25	25	12	15
Credit	20	10	47	67
City Pass	15	32	33	0
TOTAL

(1) (5 points) Complete the contingency table, filling in the column and row totals.

(2) (5 points) What is the probability that a randomly selected respondent usually pays with

credit if they take a taxi? Type the answer and any work below.

(3) (5 points) What is the probability that a randomly selected respondent pays with cash or

takes Rail? Type the answer and any work below.

(4) (5 points) What is the probability that a randomly selected respondent takes a bus and pays

with a city pass? Type the answer and any work below.

(5) (5 points) Is taking an Uber independent of paying with credit? Type the answer and

any work below. You must report two probabilities and explain your reasoning to

receive credit for this answer.

PROBABILITY THEORY: WORD PROBLEMS

Sarah is the owner of Sarah’s Pub, and her best business is on Friday and Saturday nights when customers buy plenty of alcoholic beverages (alcohol). After studying a large sample of receipts from Friday and Saturday nights, Sarah knows the following. 73% of her orders on these nights involve at least one alcohol sale. 23% of her customers order only alcohol, 28% have dinner plates, and the rest have sandwiches.   Of those who order dinner plates, 60% order alcohol; and of those who order sandwiches, 89% order alcohol. Sarah still has questions, as do I.

1. (5 points) What is the probability that a randomly selected customer orders a sandwich?

Type the answer and any work below. Write one sentence interpreting the result.

2. (5 points) What is the probability a randomly selected customer ordered alcohol and a

sandwich? Type the answer and any work below. Write one sentence

interpreting the result.

3. (5 points) What is the probability a randomly selected customer ordered alcohol or a

sandwich? Type the answer and any work below. Write one sentence

interpreting the result.

4. (5 points) What is the probability a randomly selected orders alcohol and a dinner plate? Type

the answer and any work below. Write one sentence interpreting the result.

5. (5 points) Are orders for alcohol and orders for dinner plates independent events? Type the

answer and any work below. You must report two probabilities and explain your

reasoning to receive credit for this answer.

DISCRETE DISTRIBUTIONS

AMC Inc. evaluates divisional managers in part by the number of consumer complaints senior management receives every month. The expectation is that no more than 20 complaints per division per month should be flagged for corporate attention. A sample of divisional data for the last five years or 60 months was collected. AMC defined X to be a random variable counting the number of complaints when twenty or more complaints in any division required senior management attention in a month; f(X) is the relative frequency of X. 30% of all complaints requiring corporate attention fell into this category and were included in the sample.

OPEN THE EXCEL EXAM TWO FILE. THE SPREADSHEET FOR THIS PROBLEM IS FOUND ON SHEET ONE. COMPLETE AND SAVE YOUR WORK IN EXCEL AND ENTER THE SOLUTIONS BELOW.

1. (5 points) What is the probability that X = 21? In one sentence, explain how you know.

2. (5 points) What is the probability that more than 24 complaints are received per month?

Type the answer and any work below.

3. (5 points) What is the probability that fewer than 24 complaints are received per month?

Type the answer and any work below.

4. (5 points) How many complaints in this sample are expected per month?

Type the answer below. Is your answer the expected number of all complaints that

required corporate attention each month? Write one sentence, explaining your answer.

5. (5 points) What is the standard deviation of complaints of more than 20 per quarter requiring

corporate attention? Type the answer below.

Answer 1

1)

	TAXI	BUS	RAIL	UBER	TOTAL
CASH	25	25	12	15	77
CREDIT	20	10	47	67	144
CITY PASS	15	32	33	0	80
TOTAL	60	67	92	82	301

2)

Probability = 20/60 = 1/3 = 0.33

3)

Probability = 77+92-12 /301 = 157/301

= 0.5216

4)

Probability = 32/301

= 0.1063

5)

A= Probability of taking uber = 82/301

B =Probability of paying with credit= 144/301

P(A) .P(B) = 82/301 * 144/301 = 0.1303

Probability of both= 67/301 = 0.2226

Since both are not equal, not independent.

Please revert in case of any doubt.

Please upvote. Thanks in advance