﻿ Binomial Probability Worksheet | Problems & Solutions

# Binomial Probability Worksheet

Binomial Probability Worksheet
• Page 1
1.
Edward took 16 mock tests. In 3 of the tests, his score is average. In 2 of the tests, his score is above average and in 5 of the tests his score is below average. In the remaining 6 tests his score is good. Which frequency distribution is appropriate for his test scores?

 a. Table 1 b. Table 2 c. Table 3 d. Table 4

#### Solution:

Frequency of average scores is 3.

So, place 3 tally marks in the corresponding row.

Frequency of below average scores is 5.

So, place 5 tally marks in the corresponding row.

Frequency of above average scores is 2.

So, place 2 tally marks in the corresponding row.

Frequency of good scores is 6.

So, place 6 tally marks in the corresponding row.

The frequency distribution obtained will be as shown in the table 2.

2.
Which of the following statement(s) is/are true?
I. On a pareto chart, the frequencies should be represented on the $y$ - axis.
II. In a frequency distribution, the number of classes should be between 5 and 20.
III. The three types of frequency distributions are histograms, frequency polygons and ogives.
 a. I and II only b. II only c. III only d. all are true

#### Solution:

On a pareto chart, the qualitative or categorical data is represented on the x - axis and frequencies are represented on the y - axis.

In a frequency distribution, there should be between 5 and 20 classes. Although there is no hard-and-fast rule for the number of classes contained in a frequency distribution, it is of the atmost importance to have enough classes to present a clear description of the collected data.

The three types of frequency distributions are the categorical frequency distribution, the grouped frequency distribution and the ungrouped frequency distribution.

So, only statements I and II are true.

3.
A jewellery store sells gold chains, pendants and bracelets. The cost of 24 different gold bracelets (of the same weight) are $150,$100, $150,$200, $150,$100, $150,$100, $150,$100, $150,$100, $150,$100, $150,$200, $100,$150, $150,$100, $150,$200, $150 and$200. Make a frequency distribution for the data.

 a. Table 1 b. Table 2 c. Table 3 d. Table 4

#### Solution:

In the data, the different costs are $100,$150 and \$200.

Mark the number of occurences of each data value as tally.

The frequency distribution obtained will be as shown in the table 3.

4.
Mr. Craig made a frequency distribution for the scores secured by his students in a test.
 Score Number of students Below 75 9 76 - 80 19 81 - 85 3 86 - 90 5 91 - 95 3 96 - 100 1

How many students got more than 85 points?
 a. 12 b. 19 c. 9 d. 5

#### Solution:

The number of students who scored above 85 points = number of students who scored 86 to 90 points + students who scored 91 to 95 points + students who scored 96 to 100 points = 5 + 3 +1 = 9
[Substitute the values from the table.]

So, the number of students who got more than 85 points is 9.

5.
Recognize the false statement(s).
I. The numbers used to separate the classes, so that there are no gaps in the frequency distribution are called class limits.
II. Class width for a class is found by subtracting the lower class limit from the upper class limit.
III. Class midpoint is obtained by adding the lower and upper boundaries and dividing by 2.
IV. The class limits should have the same decimal place value as the data, but the class boundaries should have one additional place value.
 a. II only b. I and II c. III and IV d. I only

#### Solution:

The numbers used to separate the classes so that there are no gaps in the frequency distribution are called class boundaries (class boundaries are different from class limits).

The class width for a class is found by subtracting the lower class limit of one class from the lower class limit of the next class.

Class midpoint is obtained by adding the lower and upper boundaries and dividing by 2.

The class limits should have the same decimal place value as the data, but the class boundaries should have one additional place value.

6.
What type of distribution does the table represent?
 Age Below 10 10 - 20 21 - 31 32 - 42 43 - 53 54 - 64 65 and above

 a. categorical frequency distribution b. continous frequency distribution c. ungrouped frequency distribution d. open - ended frequency distribution

#### Solution:

The table shown, has no specific beginning value or no specific ending value.

The frequency distribution for age is open - ended for the first class, which means that anybody below 10 years will be tallied in the first class.

It is open - ended for the last class, which means that anybody who is 65 years or older will be tallied in the last class.

So, the distribution is called an open - ended distribution.

7.
The velocity (m/sec) of water flow in a pipe of 25 m diameter for consecutive days of a month are observed as:
 1.5 1.5 1.6 1.4 1.5 1.4 1.6 1.4 1.5 1.3 1.4 1.3 1.4 1.5 1.7 1.6 1.5 1.5 1.5 1.4 1.3 1.5 1.5 1.6 1.7 1.5 1.4 1.4 1.4 1.5

Find the class boundaries for the last class by constructing an ungrouped frequency distribution.
 a. 1.7 b. 1.65 - 1.75 c. 1.6 - 1.7 d. 1.55 - 1.75

#### Solution:

Range of the data =1.7 - 1.3 = 0.4

Since the range of the data set is small, use discrete data for the classes.

The classes are 1.3, 1.4, 1.5, 1.6 and 1.7.

The class boundaries, tally marks and the frequency for each class (number of tally marks) are shown in the table.

The class boundaries for the last class is 1.65 - 1.75.

8.
The HR manager for a company asked its employees to give the details about their residing places. The details obtained by him are categorized into places as recorded: A = Atkinson Square, C = Caribbean Point, D = Dream Valley, E = Environ Enclave, T = Township, M = Montessori Enclave.
 A T E C A M D A M M E C E M C M T T E D A M M T T

Which of the following tables represents the frequency distribution of the above data? From which place the employees are more?

 a. Figure 3; Township b. Figure 2; Environ Enclave c. Figure 4; Montessori Enclave d. Figure 1; Township

#### Solution:

Since the data are categorical, discrete classes can be used. There are six places: A, E, D, T, C and M.

The class, tally marks and the frequency for each class (number of tally marks) are shown in the table.

From the frequency distribution, more people are coming from Montessori Enclave.

Figure 4 represents the frequency distribution for the given data.

9.
The students of Environmental studies collected the data of the life span of Zebras from the zoological authorities which are as follows.
20, 12, 19, 22, 28, 30, 17, 25, 10, 23, 16, 18, 21, 32, 15, 14, 8, 22, 11, 13, 18, 20, 21, 19, 19
Find the average life span of a Zebra by constructing a frequency distribution table.
 a. 18 to 22 b. 20 to 25 c. 32 years d. 15 to 20

#### Solution:

Range of the data = higher value - lower value = 32 - 8 = 24

Width = Rangenumber of classes = 24 / 5 = 4.8 5
[Assume the number of classes as 5.]

Constuct the class limits (life span of zebras) with width 5, so that the least and highest values has been included.

The class limits, boundaries, tally marks and the frequency for each class (number of tally marks) are shown in the table.

From the frequency distribution table, the average life span of Zebra is 18 to 22.
[Since the class 18 - 22 has maximum frequency.]

10.
Which among the following statement(s) is/are true about histograms?
I. Midpoints are useful in determining class widths and class boundaries.
II. Histograms are useful in displaying cumulative frequencies.
III. Histograms are used to display categorical data.
IV. Histograms are not used to represent continuous data.
 a. I and II b. II and III c. I, II and IV d. all are true

#### Solution:

The class width and class boundaries of a histogram can be determined by calculating the difference between the midpoints of adjacent classes.

Histograms can represent either frequency or cumulative frequency.

Histograms are not used for categorical data.

Histograms are used to represent continuous data.

Therefore, statements I and II are true.