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daily sales at kstore throughout уear a probability approximately with mean = $1530 and standard deviation = $120. The bookstore must have a monthly average of at least $1500 to break even. Assuming a month has 30 days, what is the probability that, for a given month, the bookstroe breaks even? That is, find P(>1500) Note: round your answer to TWO DECIMAL places. QUESTION 9 On a particular stretch of highway, the State Police know that the average speed is 62 mph with a standard deviation of 5 mph. On a busy holiday weekend, the police are concerned that people travel too fast. So they randomly monitor speeds of a sample

daily sales at kstore throughout уear a probability approximately with mean = $1530 and standard deviation = $120. The bookstore must have a monthly average of at least $1500 to break even. Assuming a month has 30 days, what is the probability that, for a given month, the bookstroe breaks even? That is, find P(>1500) Note: round your answer to TWO DECIMAL places. QUESTION 9 On a particular stretch of highway, the State Police know that the average speed is 62 mph with a standard deviation of 5 mph. On a busy holiday weekend, the police are concerned that people travel too fast. So they randomly monitor speeds of a sample

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Question 5** Continue the exercise as stated in Question 3 with the Uniform distribution, but increase the sample size from n=2 to n=30. Again, start with a clear worksheet. This time generate 300 rows of data store in C1-C30. Now each row represents a sample of n=30 data points from the population. Calculate the sample average for each of these 300 rows of data using the ROW STATISTICS command and store the results in C31. Rename the C31 as \(\bar{x}_{n=30}\). What you have created in C31 represents a Sampling Distribution of \(\bar{x}\). Calculate the DESCRIPTIVE STATISTICS of column C31. Which of the following statement/s is/are true? - [ ] I. Since the true population data is NOT from NORMAL, the central limit theorem does not apply here. - [ ] II. The mean of Column C31 is close to μ which is 100. - [ ] III. The standard deviation of Column C3 is close to \(\frac{\sigma}{\sqrt{n}}\) which is about 3.16. - [ ] IV. The standard deviation of Column C3 is close to σ which is 17.3. --- **Question 6** Create histograms for C1 (i.e. the population data) and C31 (i.e. the sample means) on the SAME Y and SAME X, including bins by clicking on the check boxes. Now both histograms will have the same scale. Save the histograms for C1 and C31 as "Fig3a.png" and "Fig3b.png", respectively, in your preferred local folder. Which of the following statement/s is/are true? - [ ] I. Both histograms are centered around 100. - [ ] II. Both graphs are approximately normal in shape. - [ ] III. The histogram of the sample means is roughly symmetric. - [ ] IV. The histogram of the sample means is more concentrated (less spread out) than the histogram of the population data. --- **Question 7** Based on your findings in Questions 3-6 (including the graphs "Fig2a.png", "Fig2b.png", "Fig3a.png", and "Fig3b.png"), answer whether the following statement is true/false. When we increase the sample size, the distribution of the sample mean \(\bar{x}\
Transcribed Image Text:**Question 5** Continue the exercise as stated in Question 3 with the Uniform distribution, but increase the sample size from n=2 to n=30. Again, start with a clear worksheet. This time generate 300 rows of data store in C1-C30. Now each row represents a sample of n=30 data points from the population. Calculate the sample average for each of these 300 rows of data using the ROW STATISTICS command and store the results in C31. Rename the C31 as \(\bar{x}_{n=30}\). What you have created in C31 represents a Sampling Distribution of \(\bar{x}\). Calculate the DESCRIPTIVE STATISTICS of column C31. Which of the following statement/s is/are true? - [ ] I. Since the true population data is NOT from NORMAL, the central limit theorem does not apply here. - [ ] II. The mean of Column C31 is close to μ which is 100. - [ ] III. The standard deviation of Column C3 is close to \(\frac{\sigma}{\sqrt{n}}\) which is about 3.16. - [ ] IV. The standard deviation of Column C3 is close to σ which is 17.3. --- **Question 6** Create histograms for C1 (i.e. the population data) and C31 (i.e. the sample means) on the SAME Y and SAME X, including bins by clicking on the check boxes. Now both histograms will have the same scale. Save the histograms for C1 and C31 as "Fig3a.png" and "Fig3b.png", respectively, in your preferred local folder. Which of the following statement/s is/are true? - [ ] I. Both histograms are centered around 100. - [ ] II. Both graphs are approximately normal in shape. - [ ] III. The histogram of the sample means is roughly symmetric. - [ ] IV. The histogram of the sample means is more concentrated (less spread out) than the histogram of the population data. --- **Question 7** Based on your findings in Questions 3-6 (including the graphs "Fig2a.png", "Fig2b.png", "Fig3a.png", and "Fig3b.png"), answer whether the following statement is true/false. When we increase the sample size, the distribution of the sample mean \(\bar{x}\
**Question 8** The daily sales at the campus bookstore throughout the school year have a probability distribution that is approximately normal with mean = $1530 and standard deviation = $120. The bookstore must have a monthly average of at least $1500 to break even. Assuming a month has 30 days, what is the probability that, for a given month, the bookstore breaks even? That is, find P(X̄ > 1500). *Note: round your answer to TWO DECIMAL places.* (Answer Box) --- **Question 9** On a particular stretch of highway, the State Police know that the average speed is 62 mph with a standard deviation of 5 mph. On a busy holiday weekend, the police are concerned that people travel too fast. So they randomly monitor speeds of a sample of 50 cars and record an average speed of 66 mph. Use central limit theorem to calculate μₓ̄ = (Input Box) and σₓ̄ = (Input Box). --- **Question 10** Using **Question 9**, find the probability that the average speed of the sample is 66 mph or greater, assuming that the average speed of all cars is 62 mph? Based on your answer, answer whether the following statement is True/False. It is very unlikely to get a sample average of 66 mph or more if, in fact, the true population average is 62 mph. (O) True ( ) False
Transcribed Image Text:**Question 8** The daily sales at the campus bookstore throughout the school year have a probability distribution that is approximately normal with mean = $1530 and standard deviation = $120. The bookstore must have a monthly average of at least $1500 to break even. Assuming a month has 30 days, what is the probability that, for a given month, the bookstore breaks even? That is, find P(X̄ > 1500). *Note: round your answer to TWO DECIMAL places.* (Answer Box) --- **Question 9** On a particular stretch of highway, the State Police know that the average speed is 62 mph with a standard deviation of 5 mph. On a busy holiday weekend, the police are concerned that people travel too fast. So they randomly monitor speeds of a sample of 50 cars and record an average speed of 66 mph. Use central limit theorem to calculate μₓ̄ = (Input Box) and σₓ̄ = (Input Box). --- **Question 10** Using **Question 9**, find the probability that the average speed of the sample is 66 mph or greater, assuming that the average speed of all cars is 62 mph? Based on your answer, answer whether the following statement is True/False. It is very unlikely to get a sample average of 66 mph or more if, in fact, the true population average is 62 mph. (O) True ( ) False
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