Calculating the Mean or Expected Value of the Sum of Two Random Variables

  • 1.

    John traveled from his house to the park and then to school every day. In a week, the distance traveled from his house to the park has a mean of {eq}25 \text{ km} {/eq}. And, the distance he traveled from the park to the school has a mean of {eq}32 \text{ km} {/eq}. What is the expected value of the total distance that he traveled in a week?

    Answers:

    • {eq}9.3\text{ km } {/eq}

    • {eq}28.5\text{ km } {/eq}

    • {eq}7\text{ km } {/eq}

    • {eq}57\text{ km } {/eq}

  • 2.

    Michael has two teams to mow his lawn. Team 1 mows at the mean of {eq}10000\text{ sq. ft}, {/eq} and team 2 mows at the mean of {eq}12000\text{ sq. ft} {/eq} within 5 hours. What is the expected value of the total square feet of lawn that mow by both teams?

    Answers:

    • {eq}1000\text{ sq.ft } {/eq}

    • {eq}2000\text{ sq.ft } {/eq}

    • {eq}11000\text{ sq.ft } {/eq}

    • {eq}22000\text{ sq.ft } {/eq}

  • 3.

    In the amusement park, the adult tickets sold have a mean of {eq}2230 {/eq}, and the children's tickets sold have a mean of {eq}1054 {/eq} in a month. Find the expected value of the total tickets that have been sold in a month.

    Answers:

    • 1176

    • 3284

    • 3824

    • 1642

  • 4.

    An ice cream machine can make two different flavors of ice cream at a time. It produces a mean of {eq}80 {/eq} cones of ice cream in one flavor and a mean of {eq}90 {/eq} cones of ice cream in another flavor in 6 hours. What is the excepted value of ice cream that the machine can make in both flavors in 6 hours?

    Answers:

    • 170

    • 150

    • 10

    • 85

  • 5.

    Mary goes shopping every weekend. This month, she bought clothes for a mean of {eq}\$200 {/eq} and other cosmetics at a mean of {eq}\$800 {/eq}. Determine the expected value of her total purchase in a month.

    Answers:

    • {eq}\$500 {/eq}

    • {eq}\$900 {/eq}

    • {eq}\$600 {/eq}

    • {eq}\$1000 {/eq}

  • 6.

    In a mill, the mean of grinding grains is {eq}30\text{ tons} {/eq} in the day shift, and the mean of grinding grains is {eq}20\text{ tons} {/eq} in the night shift. Determine the mean value of the total grinding of grains per day.

    Answers:

    • {eq}25\text{ tons } {/eq}

    • {eq}10\text{ tons } {/eq}

    • {eq}60\text{ tons } {/eq}

    • {eq}50\text{ tons } {/eq}

  • 7.

    The mean of people buying sweet popcorns is {eq}900, {/eq} and the mean of people buying savory popcorns is {eq}1350 {/eq}. Determine the excepted value of both popcorns.

    Answers:

    • 450

    • 1125

    • 2250

    • 540

  • 8.

    A baker who bakes {eq}50 {/eq} cupcakes in chocolate and pistachio flavors. He spends money on preparing the chocolate cakes that has a mean of {eq}\$130 {/eq} and on preparing the pistachio cakes that has a mean of {eq}\$150 {/eq}. What is the expected value of money spent on both flavors of cake?

    Answers:

    • {eq}\$20 {/eq}

    • {eq}\$280 {/eq}

    • {eq}\$40 {/eq}

    • {eq}\$140 {/eq}

  • 9.

    In a vehicle showroom, the number of two-wheelers sold in the first half of the month has a mean of {eq}67 {/eq} and in the second half of the month has a mean of {eq}31 {/eq}. What is the expected value of the number of two-wheelers sold in a month?

    Answers:

    • 88

    • 98

    • 77

    • 66

  • 10.

    There are 5 houses in a building. The cost of painting the interiors of the houses has a mean of {eq}\$620 {/eq} and the exterior of the houses has a mean of {eq}\$450 {/eq}. What is the mean value of the total expense of painting the entire house?

    Answers:

    • {eq}\$355 {/eq}

    • {eq}\$535 {/eq}

    • {eq}\$1070 {/eq}

    • {eq}\$1700 {/eq}

  • 11.

    Mary bakes chocolate chip cookies and macaron cookies for a total of {eq}25 {/eq} cookies. She spends a mean of {eq}\$14.3 {/eq} for chocolate chip cookies and a mean {eq}\$25.6 {/eq} for macaron cookies. What is the expected value of money that she spent on both types of cookies?

    Answers:

    • {eq}\$ 32.2 {/eq}

    • {eq}\$ 11.3 {/eq}

    • {eq}\$ 19.5 {/eq}

    • {eq}\$ 39.9 {/eq}

  • 12.

    There are five screens in the theater. The revenue from the morning show has a mean of {eq}\$ 1725, {/eq} and the revenue from the night show has a mean of {eq}\$ 2250. {/eq} Calculate the expected value of the total revenue from both shows in a day.

    Answers:

    • {eq}\$ 837 {/eq}

    • {eq}\$ 3975 {/eq}

    • {eq}\$ 1520 {/eq}

    • {eq}\$ 870 {/eq}

  • 13.

    A delivery boy who delivers packages has a mean of {eq}81 {/eq} in the morning and has a mean of {eq}26 {/eq} in the afternoon. What is the expected value of the total packages that he delivered in a day?

    Answers:

    • 107

    • 55

    • 22

    • 170

  • 14.

    The mean of selling veg pizzas is {eq}35, {/eq} and the mean of selling non-veg pizzas is {eq}45. {/eq} Calculate the total mean value for both pizzas.

    Answers:

    • 140

    • 80

    • 55

    • 125

  • 15.

    Rackie spends a mean of {eq}\$ 53 {/eq} for his indoor garden and a mean {eq}\$ 73 {/eq} for his outdoor garden. What is the expected value of money that he spent on the entire garden work?

    Answers:

    • {eq}\$ 111 {/eq}

    • {eq}\$ 126 {/eq}

    • {eq}\$ 20 {/eq}

    • {eq}\$ 63 {/eq}

  • 16.

    Jack owns both vegetarian and non-vegetarian hotels. His weekly earning from the vegetarian hotel has a mean of {eq}\$2780, {/eq} and his weekly earning from the non-vegetarian hotel has a mean of {eq}\$3950. {/eq} How do you find the total mean value of his weekly earnings from both hotels?

    Answers:

    • {eq}\$ 6730 {/eq}

    • {eq}\$ 1237 {/eq}

    • {eq}\$ 6530 {/eq}

    • {eq}\$ 1345 {/eq}

  • 17.

    Jim has invested his money in stock {eq}A {/eq} and stock {eq}B. {/eq} After a month, he earns money from stock {eq}A {/eq} has a mean of {eq}\$ 350, {/eq} and he earns money from stock {eq}B {/eq} has a mean of {eq}\$ 600. {/eq} How much is the expected value of total earnings from both stocks?

    Answers:

    • {eq}\$ 750 {/eq}

    • {eq}\$ 300 {/eq}

    • {eq}\$ 450 {/eq}

    • {eq}\$ 950 {/eq}

  • 18.

    An old man is selling handbags and back bags. His monthly earnings from selling handbags has a mean of {eq}\$ 147, {/eq} and selling back bags has a mean of {eq}\$ 234. {/eq} Calculate the total expected value of his monthly earnings.

    Answers:

    • {eq}\$ 187.3 {/eq}

    • {eq}\$ 365 {/eq}

    • {eq}\$190.5 {/eq}

    • {eq}\$ 381 {/eq}

  • 19.

    In a class test, the mean score of the boys is {eq}18, {/eq} and the mean score of the girls is {eq}27. {/eq} Find the expected value of the total score of the students.

    Answers:

    • 54

    • 22.5

    • 28.9

    • 45

  • 20.

    In a school, the students who like to play indoor games has a mean score of {eq}185.8, {/eq} and the students who like to play outdoor games has a mean score of {eq}279.3. {/eq} Find the expected value of the total score of the students.

    Answers:

    • 465.1

    • 527.8

    • 325.8

    • 678.2

  • 21.

    A woman is selling small-size and large-size pizzas. Her monthly earnings from selling small-size pizzas has a mean of {eq}49, {/eq} and selling larger-size pizza has a mean of {eq}94 {/eq}. Find the expected value of the total of her monthly earnings.

    Answers:

    • 71.5

    • 134

    • 143

    • 75.1

  • 22.

    From first grade to eighth grade, the number of girls studying in each class has a mean of {eq}500 {/eq}, and the number of boys studying in each class has a mean of {eq}700 {/eq}. Calculate the expected value of the total students studying in first grade to eighth grade.

    Answers:

    • 600

    • 1200

    • 200

    • 900

  • 23.

    Leena owns two different shops. Her monthly earning from one shop has a mean of {eq}\$2250 {/eq} and her monthly earning from another shop has a mean of {eq}\$1200 {/eq}. What is the mean of her total monthly earnings?

    Answers:

    • {eq}\$3450 {/eq}

    • {eq}\$1050 {/eq}

    • {eq}\$3500 {/eq}

    • {eq}\$1725 {/eq}

  • 24.

    In a showroom, in a month, the number of two-wheelers sold has a mean of {eq}100 {/eq} and the number of four-wheelers sold has a mean of {eq}300 {/eq}. Calculate the expected value of the total vehicles sold in a month?

    Answers:

    • 450

    • 800

    • 400

    • 850

  • 25.

    Given that the random variable {eq}x {/eq} has a mean of {eq}11.48 {/eq}, and the variable {eq}y {/eq} has a mean of {eq}16.52 {/eq}. Calculate the mean value of the sum of both random variables.

    Answers:

    • 26

    • 28

    • 11

    • 14

  • 26.

    Suppose {eq}x {/eq} and {eq}y {/eq} are two random variables in a sample. The variable {eq}x {/eq} has a mean of {eq}163 {/eq}, and the variable {eq}y {/eq} has a mean of {eq}111 {/eq}. Calculate the total expected value of the sum of two random variables?

    Answers:

    • 231

    • 129

    • 132

    • 274

  • 27.

    Consider that {eq}x {/eq} and {eq}y {/eq} are random variables in a sample. The mean value of the random variable {eq}x {/eq} is {eq}340, {/eq} and the random variable {eq}y {/eq} is {eq}430 {/eq}. Determine the total mean value of the sum of two variables?

    Answers:

    • 770

    • 330

    • 660

    • 550

  • 28.

    The mean of selling the number of hot drinks is {eq}63, {/eq} and the mean of selling the number of cold drinks is {eq}76. {/eq} Determine the expected value of both drinks.

    Answers:

    • 142

    • 139

    • 68

    • 67

  • 29.

    A man is baking white and dark chocolates. He bakes white chocolates that have a mean of {eq}30.5 {/eq}, and dark chocolates that have a mean of {eq}88.2 {/eq} in a couple of weeks. Find the expected value of the total chocolates that he was baking in a couple of weeks.

    Answers:

    • 181.7

    • 56.9

    • 118.7

    • 59.6

  • 30.

    For a week, the number of two-wheelers crossing the toll road has a mean of {eq}750, {/eq} and the number of four-wheelers crossing the toll road has a mean of {eq}950 {/eq}. Calculate the expected value of both vehicles crossing the toll road in a week?

    Answers:

    • 1007

    • 1070

    • 1777

    • 1700

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