Which of the following errors can be reduced only by increasing the sample size? a. systematic error b. random sampling error c. response bias d. frame error e. selection error

The correct answer is

b. random sampling error

Step-by-step explanation:

Sampling is a statistical method of selecting a predefined number of observations  from a larger population to determine the characteristics of and to represent the larger population.

A sampling error is a type of error in statistics that is as  a result of a difference between the calculated statistical values of a selected sample and that of the entire population. A sample of a population with an error does not properly represent the statistics of the population.

By the definition of sampling in statistics, sampling error can be eliminated by Increasing the size of the sample taken from the larger population, analogous central limit theorem.

64.5 %

Step-by-step explanation:

Let's start defining the random variable X.

X : '' SAT critical reading scores from the 2014 school year for high school students in the United States ''

We know that X ~ N (μ,σ)

Where μ is the mean and σ is the standard deviation.

⇒ X ~ N (497,115)

If we want to calculate probabilities related to X we need to standardized the random variable. We do this by subtracting the mean to X and then dividing by the standard deviation. This new random variable will be ''Z'' and Z ~ N (0,1)

We can find the probabilies of ''Z'' in any standard normal table.

The cumulative distribution of ''Z'' is the function Φ where  :

Φ(a)

Now, we need to calculate the following probability :

If we standardized this :

We know that ≅ Z ⇒

⇒

Φ(2.2) - Φ(-0.41) =

⇒ 64.52% ≅ 64.5%

We find that the probability (given as a percentage) is 64.5%