Calculus and Above

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Refer to the following frequency...

Refer to the following frequency distribution for Questions 1, 2, 3, and 4.

The frequency distribution below shows the distribution for checkout time (in minutes) in MiniMart between 3:00 and 4:00 PM on a Friday afternoon.

Checkout Time (in minutes)

1.0 - 1.9 5 (Frequency)

2.0 - 2.9 6 (Frequency)

3.0 - 3.9 4 (Frequency)

4.0 - 4.9 3 (Frequency)

5.0 - 5.9 2 (Frequency)

1.What percentage of the checkout times was less than 3 minutes?

2.Calculate the mean of this frequency distribution.

3.In what class interval must the medXXXXX XXXXXe? Explain your answer. (You don’t have to find the median)

4.Assume that the largest observation in this dataset is 5.8 minutes. Suppose this observation were incorrectly recorded as 58 instead of 5.8. Will the mean increase, decrease, or remain the same? Will the median increase, decrease or remain the same? Explain your answers.

Refer to the following information for Questions 5 and 6.

A 6-faced die is rolled two times. Let A be the event that the outcome of the first roll is a 6. Let B be the event that the outcome of second roll is an odd number.

5.What is the probability that the outcome of the second roll is an odd number, given that the first roll is a 6?

6.Are A and B independent? Why or why not?

Refer to the following data to answer questions 7 and 8. Show all work. Just the answer, without supporting work, will receive no credit.

A random sample of STAT200 weekly study times in hours is as follows:

11 14 15 17 20

7.Find the standard deviation.

8.Are any of these study times considered unusual in the sense of our textbook? Explain. Does this differ with your intuition? Explain.

Refer to the following situation for Questions 9, 10, and 11.

The five-number summary below shows the grade distribution of two STAT 200 quizzes.

Minimum Q1 Median Q3 Maximum

Quiz 1 12 40 60 95 100

Quiz 2 20 35 50 80 100

For each question, give your answer as one of the following: (a) Quiz 1; (b) Quiz 2; (c) Both quizzes have the same value requested; (d) It is impossible to tell using only the given information. Then explain your answer in each case.

9.Which quiz has greater interquartile range in grade distribution?

10.Which quiz has the greater percentage of students with grades 80 and over?

11.Which quiz has a greater percentage of students with grades less than 60?

12.A random sample of 225 SAT scores has a mean of 1522. Assume that SAT scores have a population standard deviation of 300. Construct a 95% confidence interval estimate of the mean SAT scores.

Refer to the following information for Questions 13 and 14.

There are 1000 students in the senior class at a certain high school. The high school offers two Advanced Placement math / stat classes to seniors only: AP Calculus and AP Statistics. The roster of the Calculus class shows 95 people; the roster of the Statistics class shows 86 people. There are 43 overachieving seniors on both rosters.

13.What is the probability that a randomly selected senior is in exactly one of the two classes (but not both)?

14.If the student is in the Calculus class, what is the probability the student is also in the Statistics class?

Refer to the following information for Questions 15, 16, and 17.

A box contains 5 chips. The chips are numbered 1 through 5. Otherwise, the chips are identical. From this box, we draw one chip at random, and record its value. We then put the chip back in the box. We repeat this process two more times, making three draws in all from this box.

15.How many elements are in the sample space of this experiment?

16.What is the probability that the three numbers drawn are all different?

17.What is the probability that the three numbers drawn are all odd numbers?

Questions 18 and 19 involve the random variable x with probability distribution given below.

x 2 3 4 5 10

P(x) 0.1 0.2 0.4 0.1 0.2

18.Determine the expected value of x.

19.Determine the standard deviation of x.

Consider the following situation for Questions 20 and 21.

Airline overbooking is a common practice. Due to uncertain plans, many people cancel at the last minute or simply fail to show up. Capital Air is a small commuter airline. Its past records indicate that 85% of the people who make a reservation will show up for the flight. The other 15% do not show up. Capital Air decided to book 11 people for today’s flight. Today’s flight has just 10 seats.

20.Find the probability that there are enough seats for all the passengers who show up. (Hint: Find the probability that in 11 people, 10 or less show up.)

21.How many passengers are expected to show up?

22.Given a sample size of 64, with sample mean 730 and sample standard deviation 80, we perform the following hypothesis test.

H0∶ µ=750

H1: µ<750

What is the conclusion of the test at the 0.05α=level? Explain your answer

The frequency distribution below shows the distribution for checkout time (in minutes) in MiniMart between 3:00 and 4:00 PM on a Friday afternoon.

Checkout Time (in minutes)

1.0 - 1.9 5 (Frequency)

2.0 - 2.9 6 (Frequency)

3.0 - 3.9 4 (Frequency)

4.0 - 4.9 3 (Frequency)

5.0 - 5.9 2 (Frequency)

1.What percentage of the checkout times was less than 3 minutes?

2.Calculate the mean of this frequency distribution.

3.In what class interval must the medXXXXX XXXXXe? Explain your answer. (You don’t have to find the median)

4.Assume that the largest observation in this dataset is 5.8 minutes. Suppose this observation were incorrectly recorded as 58 instead of 5.8. Will the mean increase, decrease, or remain the same? Will the median increase, decrease or remain the same? Explain your answers.

Refer to the following information for Questions 5 and 6.

A 6-faced die is rolled two times. Let A be the event that the outcome of the first roll is a 6. Let B be the event that the outcome of second roll is an odd number.

5.What is the probability that the outcome of the second roll is an odd number, given that the first roll is a 6?

6.Are A and B independent? Why or why not?

Refer to the following data to answer questions 7 and 8. Show all work. Just the answer, without supporting work, will receive no credit.

A random sample of STAT200 weekly study times in hours is as follows:

11 14 15 17 20

7.Find the standard deviation.

8.Are any of these study times considered unusual in the sense of our textbook? Explain. Does this differ with your intuition? Explain.

Refer to the following situation for Questions 9, 10, and 11.

The five-number summary below shows the grade distribution of two STAT 200 quizzes.

Minimum Q1 Median Q3 Maximum

Quiz 1 12 40 60 95 100

Quiz 2 20 35 50 80 100

For each question, give your answer as one of the following: (a) Quiz 1; (b) Quiz 2; (c) Both quizzes have the same value requested; (d) It is impossible to tell using only the given information. Then explain your answer in each case.

9.Which quiz has greater interquartile range in grade distribution?

10.Which quiz has the greater percentage of students with grades 80 and over?

11.Which quiz has a greater percentage of students with grades less than 60?

12.A random sample of 225 SAT scores has a mean of 1522. Assume that SAT scores have a population standard deviation of 300. Construct a 95% confidence interval estimate of the mean SAT scores.

Refer to the following information for Questions 13 and 14.

There are 1000 students in the senior class at a certain high school. The high school offers two Advanced Placement math / stat classes to seniors only: AP Calculus and AP Statistics. The roster of the Calculus class shows 95 people; the roster of the Statistics class shows 86 people. There are 43 overachieving seniors on both rosters.

13.What is the probability that a randomly selected senior is in exactly one of the two classes (but not both)?

14.If the student is in the Calculus class, what is the probability the student is also in the Statistics class?

Refer to the following information for Questions 15, 16, and 17.

A box contains 5 chips. The chips are numbered 1 through 5. Otherwise, the chips are identical. From this box, we draw one chip at random, and record its value. We then put the chip back in the box. We repeat this process two more times, making three draws in all from this box.

15.How many elements are in the sample space of this experiment?

16.What is the probability that the three numbers drawn are all different?

17.What is the probability that the three numbers drawn are all odd numbers?

Questions 18 and 19 involve the random variable x with probability distribution given below.

x 2 3 4 5 10

P(x) 0.1 0.2 0.4 0.1 0.2

18.Determine the expected value of x.

19.Determine the standard deviation of x.

Consider the following situation for Questions 20 and 21.

Airline overbooking is a common practice. Due to uncertain plans, many people cancel at the last minute or simply fail to show up. Capital Air is a small commuter airline. Its past records indicate that 85% of the people who make a reservation will show up for the flight. The other 15% do not show up. Capital Air decided to book 11 people for today’s flight. Today’s flight has just 10 seats.

20.Find the probability that there are enough seats for all the passengers who show up. (Hint: Find the probability that in 11 people, 10 or less show up.)

21.How many passengers are expected to show up?

22.Given a sample size of 64, with sample mean 730 and sample standard deviation 80, we perform the following hypothesis test.

H0∶ µ=750

H1: µ<750

What is the conclusion of the test at the 0.05α=level? Explain your answer

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