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The daily revenue at a university snack bar has been recorded for the past five years. Records indicate that the mean daily revenue is $1200 and the standard deviation is $400. The distribution is skewed to the right due to several high volume days (football game days). Suppose that 100 days are randomly selected and the average daily revenue computed. Which of the following describes the sampling distribution of the sample mean?
a. skewed to the right with a mean of $1200 and a standard deviation of $400.
b. normally distributed with a mean of $1200 and a standard deviation of $40.
c. normally distributed with a mean of $1200 and a standard deviation of $400.
d. normally distributed with a mean of $120 and a standard deviation of $40.

Respuesta :

Answer:

b. normally distributed with a mean of $1200 and a standard deviation of $40.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Population:

Skewed to the right, mean 1200, standard deviation [tex]\sigma = 400[/tex]

Sample of 100 days:

By the Central Limit Theorem:

Approximately normal

Mean 1200

Standard deviation [tex]s = \frac{400}{\sqrt{100}} = 40[/tex]

The correct answer is given by option b.

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