2nd Summative Test in Research 9 (The Central Limit Theorem)

Which of the following statements is correct?

• The mean of the sampling distribution of the sample means is greater than the population mean.

• The mean of the sampling distribution of the sample means is less than the population mean.

• The means of the samples drawn from a population are always equal to the population mean.

• The means of the samples drawn from a population may be equal greater than or less than the population mean.

How many possible of size n=3 can be drawn from a population of size 12?

• 36

• 1728

• 144

• 220

What is the shape of the sampling distribution of the means if random samples of size n become larger?

• Left skewed

• Right skewed

• Normal

• Rectangular

A certain population has a mean of 15.4 and a standard deviation of 5.6. If random samples of size 5 is taken from this population, which of the following statements is correct?

• The mean of the sampling distribution of the sample means is equal to 15.4.

• The mean of the sampling distribution of the sample means is less than 15.4.

• The standard deviation of the sampling distribution of the sample means is 5.6.

• The standard deviation of the sampling distribution of the sample means is 15.4.

Which sample size will give a smaller standard error of the mean?

• 12

• 20

• 25

• 35

The average precipitation for the first 7 months of the year is 19.32 inches with a standard deviation of 2.4 inches. Assume that the average precipitation is normally distributed.

What is the probability that a randomly selected year will have precipitation greater than 18 inches for the first 7 months?

• 19.32 inches

• 22.4 inches

• 20.52 inches

• 15.56 inches

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?

• 400
• 40
• 25
• 8

 A group of 625 students has a mean age of 15.8 years with a standard deviation of 0.6 years.  The ages are normally distributed. What is the probability that a randomly selected student is older than 16.5 years old?

• 0.864
• 0.879
• 0.121
• None of these

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

• The Population
• The Sample
• The Sampling Distribution

The amount of fuel used by jumbo jets to take off is normally distributed with a mean of 4000 gallons and a standard deviation of 125 gallons.  What is the probability that the mean number of gallons of fuel needed to take off for a randomly selected sample of 40 jumbo jets will be less than 3950 gallons?

• .0057
• .025
• .345
• .781