Q. 2.161 - Elementary Statistics

Question

Standard Normal Distribution. One of the most important distributions in statistics is the standard normal distribution. We discuss this distribution in detail in Chapter 6.

a. Use the technology of your choice to generate a sample of 3000 observations from a variable that has the standard normal distribution.

b. Use the technology of your choice to get a relative-frequency histogram for the 3000 observations that you obtained in part (a).

c. Based on the histogram you obtained in part (b), what specific shape does the standard normal distribution have? Explain your reasoning.

Step-by-Step Solution

Answer

a) The random variables are shown.

b) The relative frequency histogram is shown.

c) The distribution is unimodal, roughly symmetric.

Part (a) Step 1: Given Information

To determine the sample of 3000 random variables.

Part (a) Step 2: Explanation

The 3000 random variables by technology are,

Part (b) Step 1: Given Information

To determine the relative frequency histogram.

Part (b) Step 2: Explanation

The frequency distribution is,

The relative frequency histogram is,

Part (c) Step 1: Given Information

To determine the shape of the normal distribution curve.

Part (c) Step 2: Explanation

By considering the given figures the distribution is unimodal, roughly symmetric.