A sample of 24 observations is taken from a population that has 150 elements. The sampling distribution of is . an. approximately normal because is always approximately normally distributed b. approximately normal because the sample size is large in comparison to the population size c. approximately normal because of the central limit theorem d. normal if the population is normally distributed

d. normal if the population is normally distributed

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean and standard deviation , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean and standard deviation .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question:

Sample size less than 30, so only will be normal if the population is normally distribution, and thus the correct answer is given by option d.

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step-by-step explanation: