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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

1 Answer

1 vote

Answer:

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

Explanation:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean
\mu and standard deviation
\sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
\mu and standard deviation
s = (\sigma)/(√(n)).

Population:


\mu = 14.5, \sigma = 2.5

Sample:

55 students, so
n = 55

Then


\mu = 55, s = (2.5)/(√(55)) = 0.34

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

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