The Central Limit Theorem

If a population is not normally distributed, the distribution of the sample means for a given sample size n will ____________.

• approach a normal distribution as n increases

• take the same shape as the population

• be negatively skewed

• be positively skewed

The mean and standard deviation of a population are 75 and 15, respectively. The sample size is 100. What is the standard error of the mean?

• 1.5

• 1.73

• 0.15

• 8

The mean and standard deviation of a population are 400 and 40, respectively. Sample size is 25. What is the mean of the sampling distribution?

• 25

• 40

• 8

• 400

Tags

CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.2

CCSS.HSS.IC.A.1

CCSS.HSS.MD.A.1

What is the standard error of the mean if the sample size is 25 with standard deviation of 16?

• 3.2

• 0.64

• 6.25

• 1.25

The weights of the eggs produced by a certain breed of hen are normally distributed with mean 65 grams and standard deviation of 5 grams. Which of the following will you use?

• Normal Distribution

• Binomial Distribution

• Discrete Probability Distribution

• Central Limit Theorem

Tags

CCSS.HSS.ID.A.4

CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.2

CCSS.HSS.IC.A.1

CCSS.HSS.MD.A.1

In a study done on the life expectancy of 500 people in a certain geographic region, the mean age at death was 72 years and the standard deviation was 5.3 years. If a sample of 50 people from this region is selected, what is the probability that the mean life expectancy will be less than 70 years?

• Binomial Distribution

• Central Limit Theorem

• Discrete Probability Distribution

• Normal Distribution

Tags

CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

The mean and standard deviation of a population are 200 and 20, respectively. What is the probability of selecting 25 data values with a mean less than 190?

• 69%

• 31%

• 0.6%

• 99%

Tags

CCSS.HSS.ID.A.4

In a metal fabrication process, metal rods are produced that have an average length of 20.5 meters with a standard deviation of 2.3 meters. A quality control specialist collects a random sample of 30 rods and measures their lengths. Suppose the resulting sample mean is 19.5 meters. Which of the following statements is true?

• This sample mean is only 1 standard deviation above the population mean.

• This sample mean is 2.38 standard deviations below what we expect.

• This sample mean is more than 3 standard deviations away from the population mean.

• This sample mean is 2.38 standard deviations above what we expect.

Tags

CCSS.HSS.ID.A.4

These symbols represent the mean and standard deviation for which of the following distributions?

• The Population

• The Sample

• The Sampling Distribution

• The Parameter

Tags

CCSS.6.SP.A.3

True or False:

The mean of the sample means is equal to the mean of the population.

• True

• False

Tags

CCSS.6.SP.A.2