Q.2.129 - Elementary Statistics

Question

Suppose that a variable of a population has a bell shaped distribution. If you take a large simple random sample from the population, roughly what shape would you expect the distribution of sample to be? Explain your answer.

Step-by-Step Solution

Answer

According to the sample distribution, it should be roughly bell-shaped.

Step 1 : Concept Introduction

Based on two factors, a bell-shaped distribution can be defined: the mean and the standard deviation. The mean identifies the center of the triangle and the standard deviation determines its height and width.

Step 2 :Explanation

In the given distribution, a large simple random sample is drawn from the population, and the variable of the population has a bell-shaped distribution.

The variable of a population is assumed to have a bell-shaped distribution and to be represented by a large simple random sample.

A simple random sample is composed of values that are chosen primarily from the middle of the population.

In this case, we can expect to see a bell-shaped distribution around the sample size. 

Thus, the sample distribution should conform to the expected shape.