(For Questions 1 to 7) The checkout times (in minutes) for 12 randomly selected customers at a large supermarket during the store’s busiest time are as follows:
4.5
|
8.5
|
6.0
|
8.0
|
11.0
|
9.5
|
12.5
|
6.5
|
10.0
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9.0
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6.5
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13.0
|
1. (2 points)(Show work)
What is the mean checkout times based on the 12 checkout times. (Round the answers to two decimal places)
2. (5 points)
(Show work)
Give a 5-number summary of the checkout time. (Round the answers to two decimal places)
3. (4 points) Prepare a frequency distribution with a class width of 2 minutes (with the first class as 4.0 – 5.9, etc.).
4. (2 points)
(Show work)
Identify the class midpoints for frequency distribution from Question 3. (Round the answers to two decimal places)
5. (3 points)
(Show work)
Construct the relative frequency distribution based on the frequency distribution from Question 3. (Round the percentage to one decimal place)
6. (3 points)
(Show work)
We usually find the mean checkout time based on the raw data. Now suppose that we don’t have the raw data, but instead, we only have the frequency distribution. Find the mean checkout time based on the frequency distribution from Question 3.(Round the answer to two decimal places) Compare your results with the "actual" mean checkout time you found in Question 1.
7. (5 points)
(Show work)
Find the standard deviation of the checkout time based on the frequency distribution from Question 3. Please show your calculation in the following table. (Round the answer to two decimal places)
Check-out time
|
Frequency f
|
Mid-point x
|
x2
|
f * x2
|
f * x
|
4.0 – 5.9
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Sum
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___________________________________________________________________
(For Questions 8, 9 & 10) To qualify for a mortgage, an applicant needs to have a good FICO credit score. We chose a random sample of 6 applicants from a local bank, and their FICO scores are 715, 750, 665, 820, 550 and 610.
8. (5 points)
(Show work)
What is the standard deviation of the FICO scores in the sample?Please show your calculation in the following table; you may not need all columns based on the formula you use. (Round the answer to two decimal places)
FICO Scorex
|
x2
|
x-mean
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(x-mean)2
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715
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750
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665
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820
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550
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610
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9. (2 points)
(Show work)
Are any of these FICO scores considered
unusual
in the sense of our textbook? Explain.
10. (2 points)
(Show work)
What is the coefficient of variation in FICO scores of the sample? (Round the answer to two decimal places)
____________________________________________________________________________
11. (4 points) Determine whether the given value is a parameter or statistics. Please explain your answer.
(a) An agency conducts a survey on the choice of vegetable by Americans. It is reported by the agency that 57% of the respondents prefers broccoli.
(b)A UMUC STAT 200 instructor randomly selected 100 students and found the average study time is 20.5 hours per week.
___________________________________________________________________________
12. (3 points) Mimi is a recent college graduate, who is considering some career opportunities. One factor that will affect her decision is how much money she is likely to make. She got salary information from Internet. Since you are taking a Statistics course, she would like to get your opinion on whether mean salary or median salary information is more useful for her. What would be your recommendation? Please explain your answer.
13. (8 points) Assume that you make random guesses for 5 true-or-false questions.
(a) (3 pts) What is the probability that you get all 5 answers correct? (Show work and write the answer in simplest fraction form)
(b) (3 pts) What is the probability of getting the correct answer in the 5th
question, given that the first four answers are all wrong? (Show work and write the answer in simplest fraction form)
(c) (2 pts) If event A is “Getting the correct answer in the 5th
question” and event B is “The first four answers are all wrong”. Are event A and event B independent? Please explain.
14. (4 points) A high school with 1000 students offers two foreign language courses : French and Japanese. There are 200 students in the French class roster, and 80 students in the Japanese class roster. We also know that 30 students enroll in both courses. Find the probability that a random selected student takes neither foreign language course. (Show work and write the answer in simplest fraction form)
15. (6 points) Imagine you are in a game show. There are 4 prizes hidden on a game board with 16 spaces. One prize is worth $4000, another is worth $1500, and two are worth $1000. You have to pay $50 to the host if your choice is not correct. Let the random variable x be the winning.
(a) (2 pts) Complete the following probability distribution. (Show the probability in fraction format and explain your work)
x
|
P(x)
|
-$50
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|
$1,000
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$1,500
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$4,000
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|
(b) (2 pts) What is your expected winning in this game? (Show work and round the answer to two decimal places)
(c) (2 pts) What is the standard deviation of the probability distribution? (Show work and round the answer to two decimal places)
16 (6 points) Mimi just started her tennis class three weeks ago. On average, she is able to return 15% of her opponent’s serves. If her opponent serves 10 times, answer the following questions:
(a) (4 pts) What is the probability that she returns at least 2 of the 10 serves from her opponent? (Show work and round the answer to 4 decimal places)
(b) (2 pts) How many serves can she expect to return? (Hint : What is the expected value?) (Show work and round the answer to 2 decimal places)
(For Questions 1 to 7) The checkout times (in minutes) for 12 randomly selected customers at a large supermarket during the store’s busiest time are as follows:
4.5
|
8.5
|
6.0
|
8.0
|
11.0
|
9.5
|
12.5
|
6.5
|
10.0
|
9.0
|
6.5
|
13.0
|
1. (2 points)(Show work)
What is the mean checkout times based on the 12 checkout times. (Round the answers to two decimal places)
2. (5 points)
(Show work)
Give a 5-number summary of the checkout time. (Round the answers to two decimal places)
3. (4 points) Prepare a frequency distribution with a class width of 2 minutes (with the first class as 4.0 – 5.9, etc.).
4. (2 points)
(Show work)
Identify the class midpoints for frequency distribution from Question 3. (Round the answers to two decimal places)
5. (3 points)
(Show work)
Construct the relative frequency distribution based on the frequency distribution from Question 3. (Round the percentage to one decimal place)
6. (3 points)
(Show work)
We usually find the mean checkout time based on the raw data. Now suppose that we don’t have the raw data, but instead, we only have the frequency distribution. Find the mean checkout time based on the frequency distribution from Question 3.(Round the answer to two decimal places) Compare your results with the "actual" mean checkout time you found in Question 1.
7. (5 points)
(Show work)
Find the standard deviation of the checkout time based on the frequency distribution from Question 3. Please show your calculation in the following table. (Round the answer to two decimal places)
Check-out time
|
Frequency f
|
Mid-point x
|
x2
|
f * x2
|
f * x
|
4.0 – 5.9
|
|
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|
|
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|
|
|
|
|
|
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|
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|
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|
Sum
|
|
|
|
|
|
___________________________________________________________________
(For Questions 8, 9 & 10) To qualify for a mortgage, an applicant needs to have a good FICO credit score. We chose a random sample of 6 applicants from a local bank, and their FICO scores are 715, 750, 665, 820, 550 and 610.
8. (5 points)
(Show work)
What is the standard deviation of the FICO scores in the sample?Please show your calculation in the following table; you may not need all columns based on the formula you use. (Round the answer to two decimal places)
FICO Scorex
|
x2
|
x-mean
|
(x-mean)2
|
715
|
|
|
|
750
|
|
|
|
665
|
|
|
|
820
|
|
|
|
550
|
|
|
|
610
|
|
|
|
|
|
|
|
9. (2 points)
(Show work)
Are any of these FICO scores considered
unusual
in the sense of our textbook? Explain.
10. (2 points)
(Show work)
What is the coefficient of variation in FICO scores of the sample? (Round the answer to two decimal places)
____________________________________________________________________________
11. (4 points) Determine whether the given value is a parameter or statistics. Please explain your answer.
(a) An agency conducts a survey on the choice of vegetable by Americans. It is reported by the agency that 57% of the respondents prefers broccoli.
(b)A UMUC STAT 200 instructor randomly selected 100 students and found the average study time is 20.5 hours per week.
___________________________________________________________________________
12. (3 points) Mimi is a recent college graduate, who is considering some career opportunities. One factor that will affect her decision is how much money she is likely to make. She got salary information from Internet. Since you are taking a Statistics course, she would like to get your opinion on whether mean salary or median salary information is more useful for her. What would be your recommendation? Please explain your answer.
13. (8 points) Assume that you make random guesses for 5 true-or-false questions.
(a) (3 pts) What is the probability that you get all 5 answers correct? (Show work and write the answer in simplest fraction form)
(b) (3 pts) What is the probability of getting the correct answer in the 5th
question, given that the first four answers are all wrong? (Show work and write the answer in simplest fraction form)
(c) (2 pts) If event A is “Getting the correct answer in the 5th
question” and event B is “The first four answers are all wrong”. Are event A and event B independent? Please explain.
14. (4 points) A high school with 1000 students offers two foreign language courses : French and Japanese. There are 200 students in the French class roster, and 80 students in the Japanese class roster. We also know that 30 students enroll in both courses. Find the probability that a random selected student takes neither foreign language course. (Show work and write the answer in simplest fraction form)
15. (6 points) Imagine you are in a game show. There are 4 prizes hidden on a game board with 16 spaces. One prize is worth $4000, another is worth $1500, and two are worth $1000. You have to pay $50 to the host if your choice is not correct. Let the random variable x be the winning.
(a) (2 pts) Complete the following probability distribution. (Show the probability in fraction format and explain your work)
x
|
P(x)
|
-$50
|
|
$1,000
|
|
$1,500
|
|
$4,000
|
|
(b) (2 pts) What is your expected winning in this game? (Show work and round the answer to two decimal places)
(c) (2 pts) What is the standard deviation of the probability distribution? (Show work and round the answer to two decimal places)
16 (6 points) Mimi just started her tennis class three weeks ago. On average, she is able to return 15% of her opponent’s serves. If her opponent serves 10 times, answer the following questions:
(a) (4 pts) What is the probability that she returns at least 2 of the 10 serves from her opponent? (Show work and round the answer to 4 decimal places)
(b) (2 pts) How many serves can she expect to return? (Hint : What is the expected value?) (Show work and round the answer to 2 decimal places)