Q.6.44 - Elementary Statistics

Question

A classic study by F. Thorndike on the number of calls to a wrong number appeared in the paper "Applications of Poisson's Probability Summation" (Bell Systems Techical Journal. Vol. 5, pp. 604-624). The study examined the number of calls to a wrong number from coin-box telephones in a large transportation terminal. Based on the results of that paper. we obtained the following percent distribution for the number of wrong numbers during a 1-minute period.

a. Construct a relative-frequency histogram of these wrong-number data.

b. Based on your histogram, do you think that the number of wrong numbers from these coin-box telephones is approximately normally distributed? Explain your answer.

Step-by-Step Solution

Answer

(a)

(b) The number of incorrect numbers dialed from these coin-box telephones is not evenly distributed. 

Part (a) Step 1: Given information

Given in the question that, A classic study by F. Thorndike on the number of calls to a wrong number appeared in the paper "Applications of Poisson's Probability Summation" (Bell Systems Technical Jour. nal. Vol. 5 , pp. 604-624). The study examined the number of calls to a wrong number from coin-box telephones in a large transportation terminal. Based on the results of that paper. we obtained the following percent distribution for the number of wrong numbers during a 1-minute period. 

 We need to construct a relative-frequency histogram of these wrong-number data.

Part (a) Step 2: Explanation

A frequency histogram is a sort of bar graph that displays the frequency, or number of times, a data set's outcome happens. To graphically show the data, it has a title, an $x$-axis, a $y$-axis, and vertical bars.

The given data is

Wrong	Percent
$0$	$17.2$
$1$	$30.5$
$2$	$26.6$
$3$	$15.1$
$4$	$7.3$
$5$	$2.4$
$6$	$0.7$
$7$	$0.1$
$8$	$0.1$

The frequency histogram of the supplied data with incorrect numbers can be produced as follows:

Part (b) Step 1: Given information

Given in the question that, A classic study by F. Thorndike on the number of calls to a wrong number appeared in the paper "Applications of Poisson's Probability Summation" (Bell Systems Techical Journal. Vol. 5. pp. 604-624). The study examined the number of calls to a wrong number from coin-box telephones in a large transportation terminal. Based on the results of that paper. we obtained the following percent distribution for the number of wrong numbers during a 1-minute period.

Based on the  histogram we need to explain  that the number of wrong numbers from these coin-box telephones is approximately normally distributed.

Part (b) Step 2: Explanation

Wrong	Percent
$0$	$17.2$
$1$	$30.5$
$2$	$26.6$
$3$	$5.1$
$4$	$7.3$
$5$	$2.4$
$6$	$0.7$
$7$	$0.1$
$8$	$0.1$

The frequency histogram of the supplied data with incorrect numbers can be produced as follows:

The form of the distribution is right skewed, as can be seen above. As a result, the number of incorrect numbers dialed from these coin-box telephones is not evenly distributed.