Q.2.37 - Elementary Statistics

Question

 An American roulette wheel contains $18$ red numbers,$18$ black numbers, and $2$ green numbers. The following table shows the frequency with which the ball landed on each color in $200$ trials.

Step-by-Step Solution

Answer

a.

b.

c.

Part (a) Step 1: Given information

Given in the question that, An American roulette wheel contains $18$ red numbers, $18$ black numbers, and $2$ green numbers. The following table shows the frequency with which the ball landed on each color in $200$ trials.

We need to obtain a relative-frequency distribution.

Part (a) Step 2: Explanation

The relative frequency can be calculated using the formula,

Relative Frequency $=\frac{\text{ Frequency }}{\text{ Number of Observations }}$

In the table below, the frequency distribution is presented.

NUMBER	Frequency	Relative Frequency
Red	$88$	$\frac{88}{200}=0.44$
Black	$102$	$\frac{102}{200}=0.51$
Green	$10$	$\frac{10}{200}=0.05$
Total	$200$	$1$

Therefore, the relative frequency distribution of the given data sets is shown in the above table.

Part (b) Step 1: Given information

Given in the question that, An American roulette wheel contains $18$ red numbers,$18$ black numbers, and $2$green numbers. The following table shows the frequency with which the ball landed on each color in $200$ trials.

 We need to draw a Pie chart.

Part (b) Step 2: Explanation

MINITAB has been used to create the pie chart.

The portion for each class in a pie chart is calculated by multiplying ${360}^0$ by the corresponding relative frequencies.

The steps of drawing a pie chart are as follows:

• Choose Graph >Pie Chart.
•  Select Chart values from table.
•  Choose NUMBERunder Categorical variable.
•  Select Frequency under Summary variables.
•  Select Labels and choose Slide Labels tab.
•  Check Category name and Percent under Label pie slices with.
•  Click OK 

Below figure  shows the pie chart for the supplied data set.

Part (c) Step 1: Given information

Given in the question that, An American roulette wheel contains $18$red numbers,$18$ black numbers, and $2$ green numbers. The following table shows the frequency with which the ball landed on each color in $200$ trials.

Part (c) Step 2: Explanation

MINITAB has been used to create the bar chart.

The steps to making a bar chart are as follows:

•  Choose Graph > Bar Chart.
•  From Bars represent, choose Values from a table.
•  Choose Simple, and click OK.
•  In Categorical variables, enter one column of FREQUENCY.
•  Choose Chart options
•  Select Show Y as Percent.
•  Click OK

The bar chart of the given data set is shown in figure below