Q. 2.16 - Elementary Statistics

Question

Random Digits. In this exercise, use technology to work Exercise $2.159$, as follows:

a. Use the technology of your choice to obtain $50$ random integers between $0$ and $9$.

b. Use the technology of your choice to get a relative-frequency histogram based on single-value grouping for the numbers that you obtained in part (a).

c. Repeat parts (a) and (b) five more times.

d. Are the specific shapes of the distributions that you obtained in parts (a)-(c) about what you expected?

e. Repeat parts (a)-(d), but generate $1000$ random integers each time instead of $50$.

Step-by-Step Solution

Answer

(a) $$\begin{gathered} 9,0,4,8,8,9,4,5,5,0,6,9,5,4,4,6,9,5,5,0,1,3,9,6,6 \\ 5,3,9,5,7,0,8,7,0,4,0,6,0,4,7,7,7,7,2,7,8,8,7,1,1 \end{gathered}$$

(b) 

(c) Parts (a) and (b) should be repeated five times.

(d) The histogram doesn't appear to be evenly distributed. 

(e) Instead of $50$ random variables, repeat portion (a) to (d) for $1000$ random variables.

Part (a) Step 1: Concept introduction

A histogram is a contains a large amount of statistical data allocation. Karl Pearson was the first to originate the expression. To generate a bitmap, partition the number of scenarios into sections and tally number of times information goes into both zone.

Part (a) Step 2: Explanation

The 50 numbers will be generated using a random variable table.

$$\begin{gathered} 9,0,4,8,8,9,4,5,5,0,6,9,5,4,4,6,9,5,5,0,1,3,9,6,6 \\ 5,3,9,5,7,0,8,7,0,4,0,6,0,4,7,7,7,7,2,7,8,8,7,1,1 \end{gathered}$$

Part (b) Step 1: Concept introduction

A histogram is a contains a large amount of statistical data allocation. Karl Pearson was the first to originate the expression. To generate a bitmap, partition the number of scenarios into sections and tally number of times information goes into both zone.

Part (b) Step 2: Explanation

The frequency distribution is 

The relative frequency histogram is 

Part (c) Step 1: Concept introduction

A histogram is a contains a large amount of statistical data allocation. Karl Pearson was the first to originate the expression. To generate a bitmap, partition the number of scenarios into sections and tally number of times information goes into both zone.

Part (c) Step 2: Explanation

Parts (a) and (b) should be repeated five times.

Part (d) Step 1: Concept introduction

A histogram is a contains a large amount of statistical data allocation. Karl Pearson was the first to originate the expression. To generate a bitmap, partition the number of scenarios into sections and tally number of times information goes into both zone.

Part (d) Step 2: Explanation

The histogram doesn't appear to be evenly distributed. 

Because the $1,2,$ and $3$ bars are significantly smaller than planned.

Part (e) Step 1: Concept introduction

A histogram is a contains a large amount of statistical data allocation. Karl Pearson was the first to originate the expression. To generate a bitmap, partition the number of scenarios into sections and tally number of times information goes into both zone.

Part (e) Step 2: Explanation

Instead of  random variables, repeat portions (a) to (d) for $1000$ random variables.