﻿ Random Probability Distribution Worksheet | Problems & Solutions Random Probability Distribution Worksheet

Random Probability Distribution Worksheet
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1.
The dot plot shows the number of chocolates each student of a class has. How many more chocolates does David have than Joe? Who among the following has median number of chocolates?  a. 4, Joe b. 3, Robin c. 0, Suzane d. 5, Catherine

Solution:

The number of dots above each name indicate the number of chocolates each student has.

From the plot, the number of chocolates David has = 9
[Count the number of dots above the name David.]

The number of chocolates Joe has = 4
[Count the number of dots above the name Joe.]

The difference between the number of chocolates David and Joe have = 9 - 4 = 5
[Subtract 4 from 9.]

So, David has 5 chocolates more than Joe.

Median is the midpoint of the data array.

Arrange the data in increasing order
4, 5, 6, 7, 8, 9, 10

The mid point of the data set is 7. Since, Catherine has 7 chocolates, she has the median number of chocolates.

2.
Calculate the percentage raise in the number of vehicle registrations from 1990 to 2000 from the graph.  a. 10 % b. 10.53 % c. 9.09% d. 15.78 %

Solution:

Number of vehicles registered in the year 2000 = 220 million.

Number of vehicles registered in the year 1990 = 200 million.

The percentage increase = Increase in the number of vehicles original number of vehicles × 100.

So, percentage raise in vehicle registrations from 1990 to 2000 = (220Ã¢â‚¬â€œ200) / 200× 100 = (20 / 200) × 100 = 10%.

3.
The total revenue of five companies are represented in the bar graph. What is the difference between the revenue earned by company B and company D?  a. $200 mil b.$50 mil c. $400 mil d.$450 mil

Solution:

The height of each bar in the graph represents the revenue earned by a particular company.

The revenue earned by company B = $150 mil. The revenue earned by company D =$600 mil.

So, the difference between the revenue earned by Company B and Company D = $600 -$150 = $450 mil. Correct answer : (4) 4. A survey conducted by the Educational Department reveals the expenditure on the secondary and high schools. Pick an appropriate bar graph which represents the data shown in the table.  Year Secondary School (in$millions) High School (in $millions) 1985 325 225 1990 361 240 1995 418 274 2000 425 277  a. Graph 1 b. Graph 2 c. Graph 3 d. Graph 4 Solution: The height of each bar in the bar graph indicates the amount spent on the schools in the corresponding year. Observe the graphs to match the heights of each bar with the values given in the table. Observe that the heights of the bars in Graph 1 matches with the values in the table. So, Graph 1 represents the data in the table. Correct answer : (1) 5. The sale of food items in U.S. for the year 2000 is shown in the table. I. What is the angle made by the sale of bevarages in the pie chart? II. Find the ratio of the percentage sale of dairy to the sale of produce. III. What fraction of sales is grain / cereals?  Food items Sales ($) Dairy 114255.50 Beverages 79807.65 Confections 76223.75 Meat/Poultry 76958.83 Seafood 51674.80 Grains/Cereals 62039.82 Condiments 50491.47 Produce 43278.18 a. 52°, 2.64 and $\frac{1}{10}$ b. 51°, 2.64 and 9 c. 51°, 3 and 9 d. 52°, 2.64 and $\frac{1}{9}$

Solution:

Sector angle for Beverages = 79807.65 / 554730 × 360° = 51.8 52°
[Angle for each item = sale of an item Total sales× 360.]

The angle made by the sale of bevarages is 52°

Percentage sale of Dairy = 114255.50 / 554730 × 100 = 20.60%
[Percentage sale of each item = sale of an item total sales × 100.]

Percentage sale of Produce = 43278.18 / 554730 × 100 = 7.8%

The ratio of the percentage of sale of dairy to the sale of produce is 20.60 / 7.8 = 2.64

Sector angle for Grains/Cereals = 62039.82 / 554730 × 360° = 40.26 40°

40 / 360 = 1 / 9th of sales is grain/cereals.

6.
The mode of transport of a group of students to the school is shown in the table.
 Mode of transport Number of students Walking 9 Train 10 Tram 6 Car 12 Bicycle 3
What fraction of the students travel by train? Find the ratio of the percentage of the students traveling by bicycle to the students walking to the school. a. $\frac{1}{4}$th and 1 : 3 b. $\frac{1}{4}$th and 3 : 1 c. $\frac{1}{10}$th and 1 : 3 d. $\frac{1}{10}$th and 3 : 1

Solution:

The total number of students using different modes of transport = 40.

The sector angle made by students traveling by train = 10 / 40 × 360 = 90°

The fraction of students traveling by train = 90 / 360 = 1 / 4

Therefore, 1 / 4th of the students travel by train.

Percentage of students traveling by bicycle = 3 / 40 × 100 = 7.5%

Percentage of students walking = 9 / 40 × 100 = 22.5%

The ratio of percentage of the students traveling by bicycle to the students walking to the school = 7.5 / 22.5 = 1 / 3

7.
The pie chart represents the expenditure on different sports by a school authority in a calender year. If the expenditure on Tennis is $880, then what is the expenditure on each sport?  a. figure 1 b. figure 4 c. figure 2 d. figure 3 Solution: The total amount spent on sports = 880 / 55 × 360 =$5760

Amount spent on Hockey = 100 / 360 × 5760 = $1600 Amount spent on Football = 160 / 360 × 5760 =$2560

Amount spent on Baseball = 45 / 360 × 5760 = \$720 So, the expenditure on each game is:

8.
The pie chart represents the expenditure of a family on different items. Answer the following questions by analyzing the pie chart.
I. Find the percentage expenditure on Fuel.
II. What fraction of expenditure is spent on Housing?
III. Find the percentage difference in the expenditure of Clothing and Others.  a. 5.56%, $\frac{1}{8}$th and 30% b. 5.56%, $\frac{1}{8}$th and 8.32% c. 6%, $\frac{1}{6}$th and 8% d. 5.56%, $\frac{1}{6}$th and 8.32%

Solution:

Percentage expenditure on Clothing = 40 / 360 × 100 = 11.1%
[Percentage of expenditure on each item = expenditure on each itemTotal expenditure × 100.]

Percentage expenditure on Fuel = 20 / 360 × 100 = 5.56%

Percentage expenditure on Others = 10 / 360 × 100 = 2.78%

The percentage expenditure on fuel is 5.56.

Housing makes a central angle of 60°.
[From the figure.]

60 / 360 = 1 / 6th of expenditure is spent on housing.

The difference in the percentage expenditure of clothing and others is 11.1% - 2.78% = 8.32%

9.
The sales of a local electronic goods store in a particular month is shown in the bar graph. What was the difference between the sales of washing machines and refrigerators in that month?  a. 40 b. 10 c. 30 d. 20

Solution:

The height of each bar in the graph represents the number of particular items sold in the month.

The height of the bar representing the number of washing machines sold = 50

The height of the bar representing the number of refrigerators sold = 30

So, the difference in the number of sales of washing machines and refrigerators in the month is 50 - 30 = 20

10.
Find the decrease in the number of birds from 1997 to 1999 from the bar graph as shown. In which year did the zoo have the least number of birds?  a. 40 and 1997 b. 10 and 1995 c. 20 and 1998 d. 50 and1999

Solution:

The height of each bar represents the number of birds in the zoo in that particular year.

The number of birds in the year 1997 is 60.

The number of birds in the year 1999 is 10.

The decrease in the number of birds from 1997 to 1999 is 60 - 10 = 50

The number of birds in the zoo in the year 1999 is the least.
[The height of the bar is small in the year 1999.]

So, in the year 1999, the zoo had the least number of birds.