The table below represents the number of portable household generators sold by 20 Gauteng-based enterprises in the fourth quarter of 2022.355066452579314219415756248695683453998 Given that the average selling price of a portable household generator was R15, 000 during the fourth quarter of 2022, what is the expected total revenue generated from the sale of the portable household generators by all the enterprises that sold at least 60 portable household generators during the quarter? Using the raw data, determine the standard deviation and coefficient of variation of the sample data. Given that the average selling price of a portable household generator was R15, 000 during the fourth quarter of 2022, what is the expected total revenue generated from the sale of the portable household generators by all the enterprises that sold at least 60 portable household generators during the quarter?2. To extract meaningful information from the data, a business analyst prepared the table of analysis shown belowClass Frequency, f Midpoint, m fm fm2 Cumulative frequency 20 < 3015253759 3751530 < 402135735257253640 < 503345148566 8256950 < 601355715393258260 < 70116571546 4759370 < 80575375281259880 < 9028517014 450100 100230 3004570230 300 Using above table: What is the mean daily distance commuted by the employees. What is the modal daily distance commuted by the employees. What is the median daily distance commuted by the employees. What is the standard deviation as a percentage of the mean daily distance commuted by the employees3. The amount of coffee dispensed into a 250 g disposable coffee cup by an automated coffee machine at a StarrBoks shop is normally distributed with a mean of 245 g and a standard deviation of 3 g. Determine the percentage of the 250 g disposable coffee cups that are expected to contain between 239 g and 249 g of coffee. Determine the percentage of the 250 g disposable coffee cups that are expected to contain less than 238 g or more than 253 g of coffee. Determine the probability that coffee dispensed into a randomly selected 250 g disposable coffee cup at the StarrBoks shop will spill. The policy at the StarrBoks shop is to dispose of, and replace, the coffee in all cases of spillage at the automated machine. Assuming the price of a 250 g cup of coffee is R25, determine the lost revenue because of coffee spillage and disposal on a particular day during which 500 people purchased a cup of coffee each at the StarrBoks shop. Suppose that the manager of the StarrBoks shop decides to recalibrate the coffee machine so that the amount of coffee dispensed is normally distributed with a mean of 246 g and a standard deviation of 2 g. Determine the percentage of the 250 g disposable coffee cups that will spill over.4. A certain type of diabetes medication is packed in bottles of 12 pills each. Historical evidence has shown that 10% of the pills are chipped during the manufacturing process. A patient has just purchased a random bottle of the pills. Determine the probability that at least two of the pills in that bottle are chipped. A patient has just purchased a random bottle of the pills. Determine the probability that at most two of the pills in that bottle are chipped.5. An education researcher has hypothesized that the final mark obtained by high school students in the grade 11 mathematics examination is predictive of the subsequent mark obtained by the students in the Matric physical science examination. The Table below represents the data for twenty randomly selected students from high schools across the Cape Province.Student RefGrade 11 Mathematics Final Year Mark (%)Matric Physical Science Mark (%)0001687221027972011989770200938504057380320166560289595401295558114852491335775705016555028285801157958402116472240550630009704922367569152395750898887220186470 Based on the education researcher’s data, determine the Pearson Correlation Coefficient. The linear regression equation obtained by the education researcher is given by the expression, y = a + bx. Determine 'a' and 'b'. If a randomly selected student obtained a final mark of 39% in his grade 11 mathematics examination, estimate the subsequent mark obtained by the student in the Matric physical science and state whether the student did pass the Matric physical science examination. Suppose that the Matric Physical Science pass mark is 50%. For the student with student Ref “1335”, the education researcher incorrectly captured a Matric physical science mark of 57%. The correct mark is 33%. Determine the new linear regression equation in the form: y = a + bx, where ‘x’ is the grade 11 mathematics examination final mark and ‘y’ is the Matric physical science mark. By taking into consideration the revised information provided in question 24, determine the expected Pearson Correlation Coefficient

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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

The table below represents the number of portable household generators sold by 20 Gauteng-based enterprises in the fourth quarter of 2022.

35	50	66	45	25	79	31	42	19	41
5	75	62	48	69	56	83	45	39	98

Given that the average selling price of a portable household generator was R15, 000 during the fourth quarter of 2022, what is the expected total revenue generated from the sale of the portable household generators by all the enterprises that sold at least 60 portable household generators during the quarter?
Using the raw data, determine the standard deviation and coefficient of variation of the sample data.

Given that the average selling price of a portable household generator was R15, 000 during the fourth quarter of 2022, what is the expected total revenue generated from the sale of the portable household generators by all the enterprises that sold at least 60 portable household generators during the quarter?

2. To extract meaningful information from the data, a business analyst prepared the table of analysis shown below

Class	Frequency, f	Midpoint, m	fm	fm2	Cumulative frequency
20 < 30	15	25	375	9 375	15
30 < 40	21	35	735	25725	36
40 < 50	33	45	1485	66 825	69
50 < 60	13	55	715	39325	82
60 < 70	11	65	715	46 475	93
70 < 80	5	75	375	28125	98
80 < 90	2	85	170	14 450	100
	100	230 300	4570	230 300

Using above table:

What is the mean daily distance commuted by the employees.
What is the modal daily distance commuted by the employees.
What is the median daily distance commuted by the employees.
What is the standard deviation as a percentage of the mean daily distance commuted by the employees

3. The amount of coffee dispensed into a 250 g disposable coffee cup by an automated coffee machine at a StarrBoks shop is normally distributed with a mean of 245 g and a standard deviation of 3 g.

Determine the percentage of the 250 g disposable coffee cups that are expected to contain between 239 g and 249 g of coffee.
Determine the percentage of the 250 g disposable coffee cups that are expected to contain less than 238 g or more than 253 g of coffee.
Determine the probability that coffee dispensed into a randomly selected 250 g disposable coffee cup at the StarrBoks shop will spill.
The policy at the StarrBoks shop is to dispose of, and replace, the coffee in all cases of spillage at the automated machine. Assuming the price of a 250 g cup of coffee is R25, determine the lost revenue because of coffee spillage and disposal on a particular day during which 500 people purchased a cup of coffee each at the StarrBoks shop.
Suppose that the manager of the StarrBoks shop decides to recalibrate the coffee machine so that the amount of coffee dispensed is normally distributed with a mean of 246 g and a standard deviation of 2 g. Determine the percentage of the 250 g disposable coffee cups that will spill over.

4. A certain type of diabetes medication is packed in bottles of 12 pills each. Historical evidence has shown that 10% of the pills are chipped during the manufacturing process.

A patient has just purchased a random bottle of the pills. Determine the probability that at least two of the pills in that bottle are chipped.

A patient has just purchased a random bottle of the pills. Determine the probability that at most two of the pills in that bottle are chipped.

5. An education researcher has hypothesized that the final mark obtained by high school students in the grade 11 mathematics examination is predictive of the subsequent mark obtained by the students in the Matric physical science examination. The Table below represents the data for twenty randomly selected students from high schools across the Cape Province.

Student Ref	Grade 11 Mathematics Final Year Mark (%)	Matric Physical Science Mark (%)
0001	68	72
2102	79	72
0119	89	77
0200	93	85
0405	73	80
3201	66	56
0289	59	54
0129	55	58
1148	52	49
1335	77	57
0501	65	55
0282	85	80
1157	95	84
0211	64	72
2405	50	63
0009	70	49
2236	75	69
1523	95	75
0898	88	72
2018	64	70

Based on the education researcher’s data, determine the Pearson Correlation Coefficient.

The linear regression equation obtained by the education researcher is given by the expression, y = a + bx. Determine 'a' and 'b'.

If a randomly selected student obtained a final mark of 39% in his grade 11 mathematics examination, estimate the subsequent mark obtained by the student in the Matric physical science and state whether the student did pass the Matric physical science examination. Suppose that the Matric Physical Science pass mark is 50%.

For the student with student Ref “1335”, the education researcher incorrectly captured a Matric physical science mark of 57%. The correct mark is 33%. Determine the new linear regression equation in the form: y = a + bx, where ‘x’ is the grade 11 mathematics examination final mark and ‘y’ is the Matric physical science mark.

By taking into consideration the revised information provided in question 24, determine the expected Pearson Correlation Coefficient

Definition Definition Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.

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