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Calculating the Variance of the Sum of Two Random Variables

  • 1.

    Mrs. Smith wanted to combine the results of students of class 5 and class 6. The mean result and standard deviation of class 5 were 69 and 2. The mean of result and standard deviation of class 6 were 73 and 1. What is the variance of the sum of two classes?

    Answers:

  • 2.

    The mean and the standard deviation of sales by the two restaurants in the last few months are $1400 and 10 and $1100 and 13 respectively. Identify the variance of the sum sales of two restaurants.

    Answers:

    • 23

    • 269

    • 69

    • 169

  • 3.

    The manager working for the airline noted that the mean of the flights booked in a year was 1200 and the standard deviation was 30. The mean of the flights booked in another year was 1000 and the standard deviation was 17. Which of the following options represents the variance of the sum of two years?

    Answers:

    • 1,189

    • 1,089

    • 611

    • 811

  • 4.

    The average weight of the students in one school is 98 pounds and that in another school is 103 pounds. The standard deviations of both the schools are 13.5 and 11.5 respectively. Choose the correct variance of the sum of weights of two schools.

    Answers:

    • 25

    • 324.25

    • 314.5

    • 2

  • 5.

    The mean result of an online test held in January was 88 with a standard deviation of 5.2. The mean of the online test held in July was 89 with a standard deviation of 4.8. Calculate the variance of the sum of two months.

    Answers:

    • 40

    • 50.08

    • 10

    • 60.08

  • 6.

    The mean of the time utilized to perform exercises by males and females in a week is 17 hours and 15 hours with standard deviations of 1 and 1.5 respectively. What is the variance of the sum of time of exercise done by males and females?

    Answers:

    • 2.25

    • 3.5

    • 3.25

    • 2.5

  • 7.

    A teacher recorded the playtime of her students in a month. She noted that mean of playtime by girls was 27 hours with a standard deviation of 1.6 and that of boys was 32 hours with a standard deviation of 2.8. Determine the variance of the sum of two categories.

    Answers:

    • 7.84

    • 10.4

    • 2.56

    • 5.28

  • 8.

    The mean of the average rainfall in the two areas is 7 mm/hour and 6.3 mm/ hour with standard deviations of 1.2 and 1.3 respectively. Which of the following options represents the variance of the sum of the rainfall of the two areas?

    Answers:

    • 2.5

    • 3.13

    • 4.13

    • 3.5

  • 9.

    The mean and the standard deviation of the scrap exported from an area in the year 2010 is 15,800 metric tonnes and 103 respectively. The mean and the standard deviation of the scrap exported from the same area in 2011 is 17,500 metric tonnes and 100 respectively. Select the variance of the sum of scrap exported in the two years.

    Answers:

    • 10,609

    • 10,709

    • 20,609

    • 203

  • 10.

    The mean of marks scored by graduates in a stat examination is 89 with a standard deviation of 2.2 and the mean of marks scored by postgraduates is 93 with a standard deviation of 1.8. Calculate the variance of the sum of graduates and postgraduates.

    Answers:

    • 4

    • 6.48

    • 8.08

    • 4.84

  • 11.

    The mean of the productivity by the male workers of a company was 93% with a standard deviation of 1.2 and that by female workers was 94% with a standard deviation of 2.1. What is the variance of the sum of productivity by both workers?

    Answers:

    • 5.85

    • 3.85

    • 6.85

    • 4.85

  • 12.

    The mean time taken by employees of a factory to examine products is 7 minutes and the standard deviation is 2. The mean time taken by employees of another factory to examine products is 8 minutes and the standard deviation is 1. Identify the variance of the sum of two factories.

    Answers:

    • 5

    • 1

    • 7

    • 3

  • 13.

    The average study time of students in Mrs. Luna's class is 4 hours 12 minutes and that of students in Mrs. Brown's is 3 hours 35 minutes. The standard deviation of both groups is 1.5 and 1.5 respectively. Which of the following options represents the variance of the sum of two classes?

    Answers:

    • 1.5

    • 4.5

    • 2.25

    • 3

  • 14.

    The mean of the burgers sold by Raven in a month was 14 with a standard deviation of 2.8 and that by his sister was 18 with a standard deviation of 1.8. Choose the variance of the sum of burgers sold by both.

    Answers:

    • 6.6

    • 8.08

    • 11.08

    • 4.6

  • 15.

    The mean of the heights of a few men was 70 inches with a standard deviation of 0.5. The mean of the heights of a few women was 65 inches with a standard deviation of 0.7. Calculate the variance of the sum of two.

    Answers:

    • 0.74

    • 0.95

    • 0.12

    • 0.99

  • 16.

    A person owns two ice cream parlors in two different cities. Mean sales per month of both shops are $1,500 and $1,900 respectively. The standard deviation of the sales is 11 and 9 respectively. What is the variance of the sum of two parlors?

    Answers:

    • 130

    • 202

    • 200

    • 20

  • 17.

    The mean of visitors to the museum in 2002 is 1980 and the standard deviation is 3. The mean of visitors in 2003 is 2061 and the standard deviation is 4.5. Determine the variance of the sum of visitors of two years.

    Answers:

    • 7.5

    • 29.25

    • 56.25

    • 35.5

  • 18.

    The mean temperature in the two areas is 40 degrees and 46 degrees with standard deviations of 2 and 1.3 respectively. Which of the following options represents the variance of the sum of temperatures in two areas?

    Answers:

    • 4.69

    • 5.69

    • 10.69

    • 1.69

  • 19.

    The mean of records of heights of trees in an area is 141 inches and in another area is 152 inches. The standard deviation in this data is 5.5 and 5 respectively. Select the correct variance of the sum of the heights of trees in the two areas.

    Answers:

    • 55.25

    • 25.25

    • 10.5

    • 110.25

  • 20.

    The mean of heights of students in grade 5 is 55 inches and the standard deviation is 1.3. The mean of heights of students in grade 6 is 59 inches and the standard deviation is 1.3. Mrs. Luisy wants to combine the results of the heights of both grades. Calculate the variance of the sum of the heights in two grades.

    Answers:

    • 6.76

    • 3.38

    • 1.69

    • 2.6

  • 21.

    The mean of selling ice creams in summer was $1,020 with a standard deviation of 7. The mean of selling in pre-winter was $105 with a standard deviation of 6. What is the variance of the sum of sales for two seasons?

    Answers:

    • 85

    • 169

    • 13

    • 55

  • 22.

    The average of the monthly sandwiches sold in a shop is 250 with a standard deviation of 13 and the average of the monthly burgers sold at the same shop is 360 with a standard deviation of 17. Identify the variance of the sum of two.

    Answers:

    • 30

    • 685

    • 458

    • 900

  • 23.

    An exam consists of two parts- mathematics and statistics. The mean of the marks scored by aspirants in mathematics is 77 with a standard deviation of 2.3. The mean of the marks in statistics is 82 with a standard deviation of 3. Which of the following options represents the variance of the sum of marks of the two categories?

    Answers:

    • 28.29

    • 28.09

    • 14.29

    • 14.09

  • 24.

    The mean of the books borrowed by the students from the library in the first six months was 58 with a standard deviation of 2. The mean of the books borrowed by the students in the other six months of the year was 49 with a standard deviation of 2.3. Choose the correct variance of the sum of books borrowed in all months.

    Answers:

    • 18.49

    • 15.29

    • 11.49

    • 9.29

  • 25.

    The mean of the pages printed by a machine in an hour is 580 with a standard deviation of 15 and the mean of the pages printed by another machine is 780 with a standard deviation of 17. Calculate the variance of the sum of pages printed by two machines.

    Answers:

    • 1,024

    • 514

    • 2

    • 32

  • 26.

    The mean of travels booked by two companies is 145 and 189. The standard deviation in data of both companies is 7 and 8.5 respectively. Calculate the variance of the sum of two companies.

    Answers:

    • 240.25

    • 15.5

    • 199.25

    • 121.25

  • 27.

    The mean of the cycles manufactured by a company in 2009 and 2010 is 188 and 205 respectively. The standard deviation of both the data is 11 and 12 respectively. Determine the correct variance of the sum of manufacturing of the two years.

    Answers:

    • 265

    • 1,089

    • 889

    • 365

  • 28.

    The mean of the marks scored in the science examination was 82 with a standard deviation of 1.5 and the mean of the marks scored in the mathematics examination was 89 with a standard deviation of 2.5. Which of the following options represents the correct variance of the sum of marks in two examinations?

    Answers:

    • 16

    • 8

    • 8.5

    • 16.5

  • 29.

    A restaurant noted the number of customers who ordered online in two weeks. The mean and standard deviation of the first week were 12 and 1 and that of the second week were 14 and 1 respectively. Which of the following options represents the variance of the sum of two weeks?

    Answers:

    • 14

    • 2

    • 13

    • 26

  • 30.

    A bread seller wanted to combine the sales for the two months. The first month had a mean of $589 sales and a standard deviation of 4.3. The second month had a mean of $856 sales and a standard deviation of 1.3. Select the variance of the sum of sales of two months.

    Answers:

    • 20.18

    • 5.6

    • 31.36

    • 26.6

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