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Calculating the Variance of the Difference of Two Random Variables

  • 1.

    The mean result and standard deviation of class 5 were 69.5 and 2. The mean result and standard deviation of class 6 were 71.5 and 1. What is the variance of the difference between the results of the two classes?

    Answers:

    • 5

    • 4

    • 3

    • 1

  • 2.

    The mean and the standard deviation of sales by a shop in January and February are $1400 and 10 and $1100 and 13 respectively. Identify the variance of the difference in sales in two months.

    Answers:

    • 269

    • 3

    • 529

    • 9

  • 3.

    A travel company notices that the mean travel booked by them in a year was 1,500 with a standard deviation of 30. The mean travel in another year was 1,200 with a standard deviation of 17. Which of the following options represents the variance of the difference of two years?

    Answers:

    • 1,569

    • 2,209

    • 1,189

    • 169

  • 4.

    The average height of the students in one school is 45 inches and that in another school is 43. The standard deviations of both the schools are 3.5 and 1.5 respectively. Choose the correct variance of the difference of heights of students in two schools.

    Answers:

    • 4

    • 14.5

    • 2

    • 20.25

  • 5.

    The mean result of some students in test 1 is 78 with a standard deviation of 2.2. The mean result of test 2 is 89 with a standard deviation of 4.8. Calculate the variance of the difference between the two tests.

    Answers:

    • 6.78

    • 19.88

    • 27.88

    • 21.78

  • 6.

    In a gym, the trainer maintains a record of the hours a person does squats and he notices that the mean of time spent by males and females in a month is 17 hours and 15 hours with standard deviations of 2 and 3 respectively. What is the variance of the difference between males and females?

    Answers:

    • 10

    • 4

    • 7

    • 13

  • 7.

    A teacher recorded the chocolates eaten by her students in a month. She noted that mean of the chocolates eaten by girls was 27 with a standard deviation of 1.6 and that of boys was 25 with a standard deviation of 2.8. Determine the variance of the difference between the two categories.

    Answers:

    • 7.4

    • 4.4

    • 10.4

    • 1.44

  • 8.

    The mean of the canned food imported by a country in two years was 21,000 metric tonnes and 24,000 metric tonnes with standard deviations of 100 and 107 respectively. Which of the following options represents the variance of the difference in two years?

    Answers:

    • 21,449

    • 7

    • 1,449

    • 207

  • 9.

    The mean and the standard deviation of the monthly expenditure by John in 2010 was $5,800 and 10 respectively and that in 2011 is $7,500 and 7 respectively. Select the variance of the difference of expenditures in the two years.

    Answers:

    • 91

    • 9

    • 51

    • 149

  • 10.

    The mean of marks scored by graduates in a stat examination is 95 with a standard deviation of 2.2 and the mean of marks scored by them in mathematics is 93 with a standard deviation of 1.8. Calculate the variance of the difference in marks.

    Answers:

    • 4.08

    • 1.6

    • 6.6

    • 8.08

  • 11.

    The mean of the leaves taken by the male workers of a company in a year was 7 with a standard deviation of 2.1 and that by female workers was 9 with a standard deviation of 1.2. What is the variance of the difference in their leaves?

    Answers:

    • 5.97

    • 2.97

    • 5.85

    • 2.85

  • 12.

    The mean time taken by employees of a wheel-producing factory to examine a wheel is 3 minutes 17 seconds with a standard deviation of 2. The mean time taken by employees of another factory to examine a wheel is 4 minutes 12 seconds with a standard deviation is 1. Identify the variance of the difference of time taken by employees of two factories.

    Answers:

    • 7

    • 1

    • 3

    • 5

  • 13.

    The average sleep hours as recorded by a nurse in the children's ward for a baby boy was 8 hours and that for a baby girl was 7 hours 30 minutes. The standard deviation of the data in both was 2.5 and 1.5 respectively. Which of the following options represents the variance of the difference in their sleeping hours?

    Answers:

    • 4.5

    • 8

    • 4

    • 8.5

  • 14.

    The mean of the sweaters knitted by Rob's mother in a month was 14 with a standard deviation of 2.8 and that by his grandmother was 8 with a standard deviation of 1.8. Choose the variance of the difference in knitting by both.

    Answers:

    • 9.04

    • 1

    • 4.6

    • 11.08

  • 15.

    The mean height of elephants in a zoo is 103 inches with a standard deviation of 0.5. The mean height of elephants in another zoo is 105 inches with a standard deviation of 0.7. Calculate the variance of the difference of two.

    Answers:

    • 0.24

    • 0.74

    • 0.04

    • 0.54

  • 16.

    The mean of the daily rewards won by Jack in online games over two months was 11 and 14. The standard deviation of the rewards was 1.4 and 1.2 respectively. What is the variance of the difference between the rewards of two months?

    Answers:

    • 3.4

    • 0.52

    • 2.52

    • 0.2

  • 17.

    The mean of visitors to a zoo in August is 280 with a standard deviation of 3. The mean of visitors in September is 261 with a standard deviation of 4.5. Determine the variance of the difference of visitors of two months.

    Answers:

    • 12.75

    • 29.25

    • 7.5

    • 2.5

  • 18.

    The mean temperature in the two areas is 43 degrees and 46 degrees with standard deviations of 2 and 1.3 respectively. Which of the following options represents the variance of the difference of temperatures in two areas?

    Answers:

    • 0.7

    • 0.49

    • 2.31

    • 5.69

  • 19.

    The mean of records of heights of trees in a garden is 147 inches and in another garden is 152 inches. The standard deviation in this data is 4.5 and 5 respectively. Select the correct variance of the difference of the heights of trees in the two gardens.

    Answers:

    • 4.75

    • 45.25

    • 34.25

    • 25.75

  • 20.

    The mean height of girls in grade 5 is 48 inches with a standard deviation of 0.3. The mean height of boys is 51 inches and the standard deviation is 0.9. Calculate the variance of the difference of the heights in two genders.

    Answers:

    • 0.9

    • 0.72

    • 0.6

    • 0.36

  • 21.

    The data about monthly sales of a home appliances company shows a mean of $178,584 with a standard deviation of 201 in 2000. For 2001, it shows a mean of $190,205 with a standard deviation of 100. What is the variance of the difference in sales for the two years?

    Answers:

    • 50,401

    • 30,401

    • 20,401

    • 40,401

  • 22.

    The average of the monthly cookies baked in a shop is 1,750 with a standard deviation of 13 and the average of the cookies baked in another shop is 2,360 with a standard deviation of 17. Identify the variance of the difference in baking between the two shops.

    Answers:

    • 458

    • 234

    • 120

    • 350

  • 23.

    Mrs. Brown took two examinations of her students. She noted that the mean grades scored in the first examination was 89% with a standard deviation of 2.8 and that of the second examination was 78% with a standard deviation of 4.8. Which of the following options represents the variance of the difference in marks in both examinations?

    Answers:

    • 24.68

    • 30.88

    • 15.2

    • 4

  • 24.

    Two universities recorded the information about time utilized by their students in online study. The mean time of students engaged with the online study was 158 hours and 145 hours in both the universities and the standard deviation of both the data was 11.9 and 10.4. Choose the correct option showing the variance of the difference of study hours between two universities.

    Answers:

    • 33.45

    • 249.77

    • 205.45

    • 133.77

  • 25.

    The mean of the books published by an organization in 2017 was 1,580 with a standard deviation of 15 and the mean of books published by the same organization in 2018 was 2,780 with a standard deviation of 17. Calculate the variance of the difference between two years.

    Answers:

    • 1,024

    • 32

    • 64

    • 514

  • 26.

    The average daily profit earned by Mr. Lee's cake shop was $560 with a standard deviation of 18 and that by his pizza shop was $890 with a standard deviation of 15. Calculate the variance of the difference between the profits in both the shops.

    Answers:

    • 549

    • 399

    • 149

    • 99

  • 27.

    The data recorded about daily rainfall in two areas shows that in the northern area the mean of the data is 2.7 mm/hour and in the southern area is 3.1 mm/ hour. The standard deviation in the record is 0.9 and 0.7 respectively. Determine the correct variance of the difference between records of the two areas.

    Answers:

    • 0.2

    • 0.81

    • 1.3

    • 0.32

  • 28.

    John maintains a record of his daily expenditure for groceries. The data of April shows the mean of $31 with a deviation of 2.4 and that of May shows the mean of $23 with a deviation of 1.8. Which of the following choices matches the correct variance of the difference between the data of two months.

    Answers:

    • 5.52

    • 9

    • 4

    • 2.52

  • 29.

    The mean daily number of customers who visited a restaurant in a week was 88 with a standard deviation of 13. The mean for another week was 98 with a standard deviation of 11. What is the variance of the difference between the number of customers in two weeks?

    Answers:

    • 108

    • 240

    • 48

    • 290

  • 30.

    A fruit salad seller notes that the first month had a daily mean sale of $787 with a standard deviation of 4.3. In the second month, he had a mean sale of $856 with a standard deviation of 1.3. Select the variance of the difference of sales of two months.

    Answers:

    • 18.38

    • 20.18

    • 16.8

    • 14.48

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