﻿ Binomial Distribution Worksheet | Problems & Solutions Binomial Distribution Worksheet

Binomial Distribution Worksheet
• Page 1
1.
The line graph shows the automobile sales from 1990 to 2000. Pick an appropriate line graph (misleading graph), which redraws the graph to show the rapid increase in the automobile sales.  a. Figure 1 b. Figure 2

Solution:

The horizontal scale in the line graph, extends from 1990 to 2000 representing each year.

So, the plot seems to be increasing very slowly.

A graph showing rapid increase can be shown either by skipping the values on the horizontal axis or by extending the vertical scale.

Among the choices, the line graph in Figure 1 seems to be increasing rapidly, as the values on horizontal axis are skipped and the vertical axis was extended.

So, Figure 1 represents the line graph, which depicts a rapid increase in the automobile sales.

2.
The stem and leaf plot represents the test scores of students out of 100. How many students got a score in the 90's on their test out of 100? How many students have taken the test?  a. 2268, 36 b. 4, 22 c. 1, 5 d. 2, 22

Solution:

The stem shows the tens and the leaf shows the ones.

From the stem and leaf plot, it is observed that 4 students got a score in the 90's on their test out of 100.

When the total number of leaves are counted, it gives the number of students who have taken the test.

So, the total number of students is 22.

3.
The number of successful heart transplantations undertaken by two major hospitals in a city for the years 1999 - 2004 is shown on a compound time series graph. Which of the following statement(s) is/are correct?
I. There is a decrease in the number of successful heart transplantations during the years 2002 and 2003 in both the hospitals.
II. The number of successful heart transplantations done by hospital A is more in the year 2003 than in the year 2002.
III. The time series graph for hospital B is declined from 1999 through 2004.  a. I and II only b. I only c. I and III only d. II only

Solution:

There is a decrease in the number of successful heart transplantations during the years 2002 and 2003 in both the hospitals. So, the 1st statement is true.

The number of heart transplantations done by hospital A in the year 2002 is 10 and the number of heart transplantations done by hospital A in the year 2003 is 8. So the 2nd statement is false.

The time series graph for hospital B is inclined radically between the years 2001 and 2002 and declined between the years 2002 and 2003. So, the 3rd statement is false.

4.
The graphs show the sales of goods in an electronic store. Which of the graphs will the store owner produce for promotional campaigns? (to get a positive impression on the customers)  a. Graph1 b. Graph 2

Solution:

A graph can mislead by lengthening or shortening the spaces between data values in order to give a certain impression.

In graph 1, the line appears to climb up very slow and in Graph 2, the line appears to be very steep.
[Both graphs have the same scale and represent the same data.]

The store owner should make a positive impression that the sales in his store were increasing very rapidly.

So, he would use the Graph 2 for promotional campaigns so that customers will have a better impression.

5.
The graph represents the scores of four students in an examination. Which of the following conclusions interpreted from the graph are incorrect?
I. Adam's score is double the score of John.
II. Tom's performance is same as that of Chris.
III. John's score is 75% of Chris score.  a. I, II and IV b. III and IV c. I, III and IV d. I and III

Solution:

In the bar graph, the vertical scale starts at 75 rather than zero.

Statement I: It appears that Adam's score is double the score of John which is not true. Adam's score is 1.118 times the score of John.

Statement II: Tom's performance is same as that of Chris.

Statement III: John's score is 94.44% of Chris score.

Statement IV: Tom has to score 5.264% of Adam's score in addition to the score he has, to reach the score of Adam.

6.
The serving speed (miles per hour) of some of the tennis players who participated in a tennis tournament are 128, 129, 130, 131, 132, 133, 134, 135, 136, 137 and 138. Which of the stem and leaf plots represents the data correctly?  a. plot 1 b. plot 2 c. plot 4 d. plot 3

Solution:

As all the numbers are three digit numbers, the digits in the hundreds and tens places will be the stems and the ones digits will be the leaves.

The stems of the data values are 12 and 13 and the leaves are 8, 9, 0, 1, 2, 3, 4, 5, 6, 7 and 8.
[All data values are greater than 120 and less than 140.]

List the unique stems and the corresponding leaves of each stem in the increasing order.

So, plot 2 is the stem and leaf plot representing the data correctly.

7.
The back to back stem and leaf plot compares the number of boys and girls who visited the science exhibition on a particular day. Find the total number of students who visited the science exhibition.  a. 140 b. 16 c. 210 d. 60

Solution:

Total number of students = number of boys of all grades + number of girls of all grades

Total number of boys of all grades = 1 + 2 + 3 + 4 + 12 + 14 + 16 = 52

Total number of girls of all grades = 1 + 2 + 4 + 6 + 7 + 11 + 18 + 19 + 20 = 88

Total number of students = 88 + 52 = 140

8.
The back-to-back stem and leaf plot represents the number of births in two cities during the last 5 weeks. Find the total number of births in the two cities.  a. 132 b. 499 c. 49 d. 375

Solution:

The combination of a stem and a leaf in the plot gives the number of births in a particular city in a particular month.

From the plot, the total number of births in City 1 = 32 + 43 + 48 + 56 + 69 = 248

The total number of births in City 2 = 38 + 41 + 51 + 57 + 64 = 251

The total number of births in both cities = 248 + 251 = 499

9.
The graph represents the weight lifting machines and their capacities (in pounds). Which of the graphs is misleading?  a. Graph 1 b. Graph 2 c. both Graph 1 and Graph 2 d. neither Graph 1 nor Graph 2

Solution:

The scale on the vertical axis in Graph 2 has been cut off.

The data values start from 200 rather than from 0.

The difference in the capacity seems much larger compared to the actual data in Graph 1.

So, Graph 2 is the misleading graph.

10.
The number of burglaries that occured in two cities during the last 5 weeks is represented on a back-to-back stem and leaf plot. Find the range of the number of burglaries that occurred in 2 cities.  a. 37, 19 b. 50, 51 c. 2, 1 d. 37, 26

Solution:

Range of the data is the difference between the maximum and the minimum data values.

The combination of the stem and the leaf in a plot gives the number of burglaries that occurred in a particular city in a particular month.

From the figure, the maximum number of burglaries that occurred in City 1 is 69 and the minimum number is 32.

= 69 - 32 = 37
So, range of the data of City 1 = Maximum value - minimum value.
[Substitute the value and subtract.]

From the figure, the maximum number of burglaries that occurred in City 2 is 64 and the minimum number is 38.

= 64 - 38 = 26
So, range of the data of City 2 = Maximum value - minimum value.
[Substitute the value and subtract.]