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Simora [160]
2 years ago
13

As the sample size becomes larger, the sampling distribution of the sample mean approaches a _____. a. binomial distribution b.

Poisson distribution c. normal probability distribution d. hypergeometric distribution
Mathematics
1 answer:
kkurt [141]2 years ago
7 0

Answer:

c. normal probability distribution

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

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

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \mu = p and standard deviation s = \sqrt{\frac{p(1-p)}{n}}

In this question:

By the Central Limit Theorem, it is a normal distribution, so option c.

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