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A sociologist is studying the number of years of education of students whose mothers have bachelor's degrees or higher. The data is normally distributed with a population mean of 14.5 years and a population standard deviation of 2.5 years. If a sample of 55 students is selected at random from the population, select the mean and standard deviation of the sampling distribution below.

a. σi= 0.05 years
b. σi= 2.5 years
c. σi= 0.34 years
d. µ= 14.5 years

Respuesta :

Answer:

The mean of the sampling distribution is 14.5 years and the standard deviation is 0.34 years.

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].

Population:

[tex]\mu = 14.5, \sigma = 2.5[/tex]

Sample:

55 students, so [tex]n = 55[/tex]

Then

[tex]\mu = 55, s = \frac{2.5}{\sqrt{55}} = 0.34[/tex]

The mean of the sampling distribution is 14.5 years and the standard deviation is 0.34 years.

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