Question

The average exam score of students of a large class is 70 with a standard deviation of 10. A sample of 36 students is selected, and the mean score of these students is computed. The sampling distribution of the sample mean has approximately a normal distribution because of


(A) the 68.3-95.4-99.7 rule.
(B) the law of large number.
(C) the central limit theorem.

Answer 1

Answer:

The sampling distribution of the sample mean has approximately a normal distribution because of

c) the central limit theorem.

Step-by-step explanation:

Given that the average exam score of students of a large class is 70 with a standard deviation of 10.

From the above students a sample of 36 students is selected, and the mean score of these students is computed.

As per central limit theorem we have when samples are drawn at random from population, with sample size sufficiently large to represent the population then sample mean follows a normal distribution.

Here population size N = 70 and sample size n =36

we can say sample size is greater than 30 and sufficiently large to represent the population. Also we can assume that these are randomly drawn.

So the answer would be

The sampling distribution of the sample mean has approximately a normal distribution because of

c) the central limit theorem.