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A random sample of 40 college students has a mean earnings of​ $3120 over the summer months. Assume the population standard deviation of earnings over the summer months for college students is​ $677 and that the distribution of earnings over the summer months for college students is normally distributed. Determine whether a normal distribution or a​ t-distribution should be used or whether neither of these can be used to construct a confidence interval.

Respuesta :

Answer:

A normal distribution or z-test is used to construct a confidence interval.

Step-by-step explanation:

We are given the following in the question:

Sample mean, [tex]\bar{x}[/tex] = $3120

Sample size, n = 40

Population standard deviation, σ = $677

The distribution of earnings of college is a normal distribution.

Conditions:

  • Since we are given the population standard deviation and the the sample size is also greater than 30.

Conclusion:

Thus, we use a normal distribution or z-test to construct a confidence interval.

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