Sampling Distribution Mean

There were 5,317 previously owned homes sold in a western city in the year 2000. The distribution of the sales prices of these homes was strongly right-skewed, with a mean of $206,274 and a standard deviation of $37,881. If all possible simple random samples of size 100 are drawn from this population and the mean is computed for each of these samples, which of the following describes the sampling distribution of the sample mean?

• Approximately normal with mean $206,274 and standard deviation $3,788

• Approximately normal with mean $206,274 and standard deviation $37,881

• Approximately normal with mean $206,274 and standard deviation $520

• Strongly right-skewed with mean $206,274 and standard deviation $3,788

• Strongly right-skewed with mean $206,274 and standard deviation $37,881

The normal curve shown represents the sampling distribution of a sample mean for sample size n = 25, selected at random from a population with standard deviation sd. Which of the following is the best estimate of the standard deviation of the population, sd ?75

• 3

• 6

• 15

• 30

• 75

A recent study was conducted to investigate the duration of time required to complete a certain manual dexterity task. The reported mean was 10.2 seconds with a standard deviation of 16.0 seconds. Suppose the reported values are the true mean and standard deviation for the population of subjects in the study. If a random sample of 144 subjects is selected from the population, what is the approximate probability that the mean of the sample will be more than 11.0 seconds?

• 0.1151

• 0.2743

• 0.7257

• 0.8849

• Based on the values of the true mean and true standard deviation, it can be concluded that the population distribution is not normal and therefore the probability cannot be calculated.

In one region of the country, the mean length of stay in hospitals is 5.5 days with standard deviation 2.6 days. Because many patients stay in the hospital for considerably more days, the distribution of length of stay is strongly skewed to the right. Consider random samples of size 100 taken from the distribution with the mean length of stay, x, recorded for each sample. Which of the following is the best description of the sampling distribution of x ?

• Strongly skewed to the right with mean 5.5 days and standard deviation 2.6 days

• Strongly skewed to the right with mean 5.5 days and standard deviation 0.26 day

• Strongly skewed to the right with mean 5.5 days and standard deviation 0.026 day

• Approximately normal with mean 5.5 days and standard deviation 2.6 days

• Approximately normal with mean 5.5 days and standard deviation 0.26 day

Researches found that boys playing high school football absorb an average of 355 hits to the head with a standard deviation of 80 hits during a season.  What is the probability on a randomly selected team of 48 players that the average number of head hits per player is between 340 and 360?

• .236

• .429

• .571

• .614

The average speed of 1500 vehicles traveled on a stretch of highway that day is 67 miles per hour with a standard deviation of 3.5 miles per hour. If 100 vehicles are randomly selected as samples, what would be the mean of the resulting sampling distribution of sample means?

• 63.5

• 67

• 70.5

• 74

The average speed of 1500 vehicles traveled on a stretch of highway that day is 67 miles per hour with a standard deviation of 3.5 miles per hour. If 100 vehicles are randomly selected as samples, what would be the standard error of the resulting sampling distribution of sample means?

• 0.52

• 0.43

• 0.34

• 0.25

What is the relationship between the mean of the population and the mean of the sampling distribution of the sample means?

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

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

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

• the mean of the population is not equal to the mean of the sampling distribution of the sample means.

A soft drink bottler claims that, on average, cans contain 12 oz. of soda. Suppose the true distribution of soda volumes is normally distributed with a mean of 12 oz. and a standard deviation of .16 oz. Sixteen cans are randomly selected and their volumes are measured. What is the probability the average volume will be between 11.96 and 12.08 oz.?

• .2902

• .8186

• .7424

• .3194

What happens to the shape of a sampling distribution of sample means as n increases?

• It becomes narrower and bimodal.

• It becomes narrower and more normal.

• It becomes wider and skewed right. 

• It becomes wider and more normal.