Mean and Standard Deviation of Sampling Distributions

For the population of farm workers in New Zealand, suppose that weekly income has a distribution with a mean of µ = $500 and a standard deviation of σ = $160. A survey of 100 farm workers is taken, including information on their weekly income. What is the probability that a randomly selected worker has an income of at most $530?

• 0.0304

• 0.9696

• 0.4591

• 0.318

• ~0

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

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

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.

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 standard deviation of a sampling distribution is the same as the standard deviation as the population.

• True

• False

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

• It becomes narrower (closer to the population's true mean) and bimodal.

• It becomes narrower (closer to the population's true mean) and more normal.

• It becomes wider (further from the population's true mean)and skewed right.

• It becomes wider (further to the population's true mean)and more normal.

When sampling from a population with proportion p, the distribution of sample proportions (p-hat) will vary. What will be the mean of all possible sample proportions?

• p

Your mail-order company advertises that it ships 90% of its orders within three working days. You select an SRS of 100 of the 5000 orders received in the past week for an audit.

What is the standard deviation?

• 0.04

• 0.004

• 0.3

• 0.03

A realtor has been told that 43% of homeowners in a city prefer to have a finished basement. She surveys a group of 300 homeowners randomly chosen from her client list. Describe the sampling distribution model of the proportion of homeowners in this sample who prefer a finished basement.

• mean = 43%; standard deviation = 1.4%

• mean = 57%; standard deviation = 2.9%

• mean = 57%; standard deviation = 1.4%

• mean = 43%; standard deviation = 2.9%

• There is not enough information to describe the distribution.