Question

A variable of a population has a left-skewed distribution.

a. If a large simple random sample is taken from the population, roughly what shape will the distribution of the sample have? Explain your answer.

b. If two simple random samples are taken from the population, would you expect the two sample distributions to have identical shapes? Explain your answer.

c. If two simple random samples are taken from the population, would you expect the two sample distributions to have similar shapes? If so, what shape would that be? Explain your answers.

Short answer

From the given information

a) The distribution shape is left-skewed shaped.

b) No. The two samples don't have identical shapes.

c) Yes, the two samples have identical shapes.

Step-by-step solution

Part (a)Step 1 : Given Information

It is given in the question that, a variable of a population has a left-skewed distribution

Part (a) Step 2: Explanation

The number of peaks in distribution, as well as its symmetry, skewness, and uniformity, are used to describe its shape.

Because the sample distribution will be roughly the same shape as the pollutant distribution, the distribution is left-skewed.

Part (b) Step 3: Given Information

It is given in the question that, a variable of a population has a left-skewed distribution

Part (b) Step 4: Explanation

The number of peaks in distribution, as well as its symmetry, skewness, and uniformity, are used to describe its shape.

Because sample distributions are approximations of population distributions, the two samples do not have identical shapes.

Part (c) Step 5: Given Information

It is given in the question that, a variable of a population has a left-skewed distribution

Part (c) Step 6: Explanation

The two samples have identical shapes because sample distributions will have about the same shape as the population distribution.