When taking a sample from a population, which of the following is true?

a. The distribution of the sample items will always follow a bell-shaped curve (such as a normal or t distribution)

b. There is a 95% chance that the sample mean will equal the population meanc.

c. We can always substitute the population variance for the sample varianced.

d. The larger the number of items in the sample, the more closely the distribution of sample items will follow a bell-shaped curve

The larger the number of items in the sample, the more closely the distribution of sample items will follow a bell-shaped curve

Step-by-step explanation:

The question is about the distribution of the sample

The sampling distribution, also called the distribution of the sample mean is the distribution for many samples drawn form population at random for large sizes.

As per central limit theorem, if samples of sufficiently large size to represent the population is drawn from the population, the sample means of all sample will follow a normal distribution and hence bell shaped.

So from the options we say a is incorrect because not always

b is incorrect because there is no mention about the chance.

c is incorrect because when we use sample variance we use t test

Option d is correct.

The larger the number of items in the sample, the more closely the distribution of sample items will follow a bell-shaped curve