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Random samples of size 17 are taken from a population that has 200 elements, a mean of 36, and a standard deviation of 8. Which of the following best describes the form of the sampling distribution of the sample mean for this situation? a. Approximately normal because the sample size is small relative to the population size b. Approximately normal because of the central limit theorem c. Exactly normal d. None of these alternatives is correct.

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Answer:

d

Step-by-step explanation:

Cricetus

None of the given alternatives described the Sample mean for the situation. A complete solution is below.

Given values are:

Sample size,

  • n = 17

Mean,

  • μ = 36

Standard deviation,

  • σ = 8

As we know,

The Standard deviation of sample mean,

→ [tex]\frac{\sigma}{\sqrt{n} }[/tex]

By substituting the values, we get

→ [tex]\frac{8}{\sqrt{17} }[/tex]

→ [tex]\frac{8}{4.13}[/tex]

→ [tex]1.94[/tex]

Thus the response i.e., "option d" is appropriate.

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