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A sample of 144 was taken from a population with a standard deviation of 36
inches. What is the margin of error for a 99.7% confidence interval?
A. 6
B. 12
C. 3
D. 9

Respuesta :

Using the z-distribution, it is found that the margin of error for a 99.7% confidence interval is of:

D. 9

What is the margin of error for a z-distribution confidence interval?

It is given by:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

  • z is the critical value.
  • [tex]\sigma[/tex] is the standard deviation of the population.
  • n is the sample size.

By the Empirical Rule, 99.7% of the measures are within 3 standard deviations of the mean, hence z = 3. The other parameters are given as follows:

[tex]\sigma = 36, n = 144[/tex].

Hence:

[tex]M = z\frac{\sigma}{\sqrt{n}} = 3\frac{36}{\sqrt{144}} = 3 \times 3 = 9[/tex]

Hence option D is correct.

More can be learned about the z-distribution at https://brainly.com/question/25890103

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