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Jacori wants to estimate the proportion on seniors who will participate in graduation. He interviews a simple random sample of 40 of the 514 seniors at his school. He find that 34 are planning to participate. Is the normal condition for finding a confidence interval met?

Respuesta :

Using the Central Limit Theorem, it is found that the condition is not met, as there are less than 10 failures.

What does the Central Limit Theorem states?

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, 34 of the 40 seniors are planning to participate in graduation, hence:

  • np = 34.
  • n(1 - p) = 6 < 10.

Since there are less than 10 failures, the normal condition for finding a confidence interval is not met.

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

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