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Data regarding average reported number of calories consumed per day is collected from a random sample of 800 CSUN students chosen using randomly selected student ID numbers. The mean reported number of calories consumed per day from the sample is found to be 2,700. What is the best estimate for the unknown population average reported number of calories consumed per day of all CSUN students?

a. 1,000
b. 2,340
c. 800
d. 2,700
e. 3,300

Respuesta :

Answer:

d. 2,700

Step-by-step explanation:

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.

The mean of the sample is 2700.

So, by the central limit theorem, the best estimate for the unknown population average reported number of calories consumed per day of all CSUN students is 2700.

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