Answered

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An exam consists of 50 multiple choice questions. Based on how much you studied, for
any given question you think you have a probability of
p = 0.70 of getting the correct answer. Consider the
sampling distribution of the sample proportion of the 50
questions on which you get the correct answer.

Sagot :

Using the Central Limit Theorem, it is found that the sampling distribution of the sample proportion of the 50 questions on which you get the correct is approximately normal, with mean of 0.7 and standard error of 0.0648.

What does the Central Limit Theorem state?

It states that for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].

In this problem, we have that p = 0.7, n = 50, hence the mean and the standard deviation are given as follows:

[tex]\mu = p = 0.7[/tex]

[tex]s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.7(0.3)}{50}} = 0.0648[/tex]

More can be learned about the Central Limit Theorem at https://brainly.com/question/24663213

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