A class has 40 students.

Thirty students are prepared for the exam, • Ten students are unprepared.

The professor writes an exam with 10 questions, some are hard and some are easy.

• 7 questions are easy. Based on past experience, the professor knows that:

– Prepared students have a 90% chance of answering easy questions correctly

– Unprepared students have a 50% chance of answering easy questions correctly.

• 3 questions are hard. Based on past experience, the professor knows that:

– Prepared students have a 50% chance of answering hard questions correctly

– Unprepared students have a 10% chance of answering hard questions correctly

• Each student’s performance on each question is independent of their performance on other questions.

(a) Find the probability that a prepared student answers all 10 questions correctly.

(b) What is the probability that at least one of the 30 prepared students answers all 10 questions correctly. Assume that each student’s score is independent of every other student.

(c) Let P be the number of questions answered correctly by a randomly chosen prepared student, and let U be the number answered correctly by a randomly chosen unprepared student. Find E[P] and E[U]

19) A die is weighted in such a way that each of 1 and 2 is three times as likely to come up as each of

the other numbers. Find the probability distribution. What is the probability of rolling an even

number?

20) Suppose you pick 1 card at random from a standard deck of 52 playing cards. Find the probability

that the card you select is between 4 and 7?

21) Suppose you pick 1 card at random from a standard deck of 52 playing cards. Find the probability

that the card you select is an “ace” or a club.

22) Suppose you pick 4 cards at random out of a deck of cards. Find the probability that

all

cards are

the same color.

Suppose that I have a bag of marbles: 2 are red, 2 are green and 1 is blue.

You select three marbles from the bag. Find the following probabilities:

23) You get both red marbles

24) You get at least

one

red marble

25) You get one of each color

26) You get no red marbles.

27) You get both red marbles, given that you got the blue marble

28) You get both red marbles, given that you did not get the blue marble.

29) Two dice are rolled – a red die and a green die.

Let event A := Neither die is a 1 or a 6 and event B:= The sum is even.

Are these events independent? How do you know?

30) It snows in Greenland an average of once every 25 days, and when it does, glaciers have a 20%

chance of growing. When it does not snow in Greenland, glaciers have only a 4% chance of growing.

What is the probability that it is snowing in Greenland when glaciers are growing?

1. According to Masterfoods, the company that manufactures M&M’s, 12% of peanut M&M’s are brown, 15% are yellow, 12% are red, 23% are blue, 23% are orange and 15% are green. (Round your answers to 4 decimal places where possible)

a. Compute the probability that a randomly selected peanut M&M is not blue.



b. Compute the probability that a randomly selected peanut M&M is blue or orange.



c. Compute the probability that three randomly selected peanut M&M’s are all yellow.



d. If you randomly select three peanut M&M’s, compute that probability that none of them are brown.



e. If you randomly select three peanut M&M’s, compute that probability that at least one of them is brown.

2.  To compute a student's Grade Point Average (GPA) for a term, the student's grades for each course are weighted by the number of credits for the course. Suppose a student had these grades:
3.6 in a 5 credit Math course
1.8 in a 3 credit Music course
2.6 in a 4 credit Chemistry course
3.2 in a 6 credit Journalism course
What is the student's GPA for that term? Round to two decimal places. Student's GPA =

3. The average student loan debt for college graduates is $25,900. Suppose that that distribution is normal and that the standard deviation is $11,400. Let X = the student loan debt of a randomly selected college graduate. Round all probabilities to 4 decimal places and all dollar answers to the nearest dollar.

a. What is the distribution of X? X ~ N( , )

b Find the probability that the college graduate has between $19,200 and $33,500 in student loan debt.

c. The middle 10% of college graduates' loan debt lies between what two numbers?
     Low: $
     High: $

1. For their uniforms, the Vikings soccer team has a choice of six different styles for the shirts, five for the shorts, and five colours for their socks. How many different uniforms are possible? A) 16 B) 150 C) 60 D) 55

2. The Niagara Ice Dogs have 4 people trying out for goal. Their coach wants to try a different goalie in each of the three periods of an exhibition game. In how many ways can the coach choose the three different goalies for the game? A) 12 B) 24 C) 7 D) 55 E) 20

3. How many arrangements of the word ALGORITHM begin with a vowel and end with a consonant? A) 18 B) 5040 C) 90720 D)181440 E) 362880

4. From a class of 14 boys and 9 girls, how many ways can I choose a committee of 6 to analyze classroom productivity with and equal number of boys and girls? A) 126 B) 252252 C) 30576 D) 448

5.A bag contains three green Christmas ornaments and four gold ornaments. If you randomly pick a single ornament from the bag, what is the probability that it will be green? A) 3/4 B)3/7 C)4/7 D)4/3

6. A bag contains three green Christmas ornaments and four gold ornaments. If you randomly pick two ornaments from the bag, at the same time, what is the probability that both ornaments will be gold?
A) 4/7 B) 2/7 C)3/7 D) none of the above

7. How many 4 digit number can be made using 0 -7 with no repeated digits allowed?
A) 5040 B) 4536 C) 2688 D) 1470

8. A coin is tossed three times. What is the probability of tossing three heads in a row?
A) 3/8 B)1/8 C)1/2 D)7/8

9. Two standard dice are rolled. What is the probability of rolling doubles (both the same number)?
A) 1/6 B)1/4 C)1/36 D) 5/36

10. There are 50 competitors in the men’s ski jumping. 30 move on to the qualifying round. How many different ways can the qualifying round be selected? A) 50! B) 30! C) 80 D) 1500 E) 1.25 × 1046

11. How many ways can the manager of a baseball team put together a batting order of his nine players, if the shortstop must bat 3rd?
A) 40320 B) 504 C) 362880 D) 120960

12. If a CD player is programmed to play the CD tracks in random order, what is the probability that it will play six songs from a CD in order from your favourite to your least favourite? A)1/6 B)2/3 C)1/720 D)5/6 E) 1/360

13. A group of eight grade 11 and five grade 12 students wish to be on the senior prom committee. The committee will consist of three students. What is the probability that only grade 12 students will be elected, assuming that all students have an equal chance of being elected?

Question

Consider the following table.

Find the standard deviation of this variable.

Homework Help:

3VA. Calculating the mean, variance, and standard deviation of discrete variables (Links to an external site.) (4:35)

3DC. Mean, expected value, variance, and standard deviation of discrete variables (Links to an external site.) (DOCX)

Group of answer choices

3.48

4.50

1.51

2.27

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Question

The standard deviation of samples from supplier A is 0.0841, while the standard deviation of samples from supplier B is 0.0926. Which supplier would you be likely to choose based on these data and why?

Homework Help:

3DD. Interpreting and comparing discrete variable standard deviations (Links to an external site.) (DOCX)

Group of answer choices

Supplier A, as their standard deviation is higher and, thus easier to fit into our production line

Supplier B, as their standard deviation is lower and, thus, easier to fit into our production line

Supplier B, as their standard deviation is higher and, thus, easier to fit into our production line

Supplier A, as their standard deviation is lower and, thus, easier to fit into our production line

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Question

Fifteen golfers are randomly selected. The random variable represents the number of golfers who only play on the weekends. For this to be a binomial experiment, what assumption needs to be made?

Homework Help:

3DE. Definitions, assumptions and elements (n, x, p) of binomial experiments (Links to an external site.) (DOCX)

Group of answer choices

The probability of being selected is the same for all fifteen golfers

All fifteen golfers play during the week

The probability of golfing on the weekend is the same for all golfers

The probability of golfing during the week is the same for all golfers

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Question

A survey found that 31% of all teens buy soda (pop) at least once each week. Seven teens are randomly selected. The random variable represents the number of teens who buy soda (pop) at least once each week. What is the value of n?

Homework Help:

3DE. Definitions, assumptions and elements (n, x, p) of binomial experiments (Links to an external site.) (DOCX)

Group of answer choices

0.07

0.31

x, the counter

7

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Question

Sixty-eight percent of US adults have little confidence in their cars. You randomly select eleven US adults. Find the probability that the number of US adults who have little confidence in their cars is (1) exactly eight and then find the probability that it is (2) more than 6.

Homework Help:

3VB. Calculating binomial probabilities and cumulative probabilities (Links to an external site.) (8:23)

3DF. Binomial probabilities versus cumulative probabilities (Links to an external site.) (DOCX)

Group of answer choices

(1) 0.753 (2) 0.256

(1) 0.753 (2) 0.744

(1) 0.247 (2) 0.256

(1) 0.247 (2) 0.744

Winnipeg district sales manager of Far End Inc. a university textbook publishing company, claims that the sales representatives makes an average of 20 calls per week on professors. Several representatives say that the estimate is too low. To investigate, a random sample of 28 sales representatives reveals that the mean number of calls made last week was 44 and variance is 2.41.

Conduct an appropriate hypothesis test, at the 5% level of significance to determine if the mean number of calls per salesperson per week is more than 40.

(a)     Provide the hypothesis statement

(b)     Calculate the test statistic value

(c)     Determine the probability value

(d) Provide an interpretation of the P-value (1 Mark)

Each day, Luke counts how many licks it takes to get the center of a candy bar. After 30 days, Luke knows the average number of licks it takes to get to the center of a candy bar is 428. Assume that the distribution of licks is normal distributed with a standard deviation of 20.

a) On day 31, it takes Luke 388 licks to get to the center of the candy bar. What is the probability that it only takes 388 licks or less to get to the center of candy bar.

b) Construct a 94% confidence interval for the number of licks it takes to get to the center of a candy bar. Give an appropriate interpretation.

c) Luke's friend guess it took 400 licks to get to the center. Is this a reasonable guess.

1. An average of 10 cars per hour arrive at a single-server drive-in teller. Assume that the average service time for each customer is 4 minutes, and both interarrival times and service times are exponential.

   1. What is the arrival rate per minute?

   2. What is the servicing rate per minute?

   3. What is the servicing rate per hour?

   4. What is the traffic intensity?

   5. What is the probability that the teller is idle?

   6. What is the average number of cars waiting in line for the teller?

   7. What is the average number of cars in the drive-in facility (waiting or serviced)?

   8. What is the average amount of time a drive-in customer spends in the facility (waiting

      or being serviced?

   9. What is the average amount of time a customer spends in the waiting line?

The number of traffic lights malfunctioning daily in any city can be said to satisfy the binomial distribution. However, the rate at which “successes” (traffic lights malfunctioning) and “failures” (traffic lights not malfunctioning) occurs nearly instantaneously, with nearly nonzero probability, such that the expected value approaches a constant. It is known that the second moments (E[X2]) of the number of daily malfunctioning traffic lights in Philadelphia, Pittsburgh, and Erie respectively are 72, 56, and 42. The malfunctioning of traffic lights between different cities is mutually independent.

Let ? = # of malfunctioning traffic lights during a day in Philadelphia, ? = # of malfunctioning traffic lights during 2 days in Pittsburgh, and ? = # of malfunctioning traffic lights during a day in Erie. Calculate P(? + ? + ? = 24).

1. Each month, a convenience store starts with four copies of the magazine, Worm Digest Monthly. Let X be the number of customers coming into the store who want to buy a copy of WDM. The distribution of X is shown in the table below.

1. What is the probability that the store will sell all four copies of WDM?
2. What is the expectation of Y = the number of copies of WDM sold by the store?
3. The store pays $3 for each copy, sells copies for $6, and sells unsold copies back to the publisher for $1.50. What is the expectation of the monthly net sales due to WDM in the store?