AP Stat Sampling Distribution Means and Proportions

Suppose the teenagers that attend public high schools get an average of 5.7 hours of sleep each night with a standard deviation of 1.7 hours.  What is the probability that a randomly selected group of 35 high school students get more than 6 hours of sleep each night?

• .430

• .148

• .281

• .087

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

The average cost for a gallon of gasoline is $2.51 (source AAA.org) with a standard deviation of $0.42. Find the mean and standard error of the sampling distribution if n = 49

• μ_x-bar = 2.51, σ_x-bar = 0.06

• μ_x-bar = 0.358, σ_x-bar = 0.06

• μ_x-bar = 0.0251, σ_x-bar = 0.06

• μ_x-bar = 2.51, σ_x-bar = 0.857

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.

Taxi fares in New York City are normally distributed with a mean fare of $22.50 and a standard deviation of $2.20. A tourism agency surveys 25 of its clients who have recently traveled to New York City to determine whether or not this information is accurate. The standard deviation of the sampling distribution for average taxi fare where the sample size is 25 is _____.

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

Would it be unusual to get a sample proportion of .35 or higher? Explain

• Yes because only 10 of the sample proportions 0.35.

• No because 23/100 of the sample proportions were 35% or higher. 23% is not unusual

• Yes because we should get 25% every time.

The actual sample proportion was 3/20 = 0.15. Is this convincing evidence that fewer than 25% of the game pieces are instant winners?

• Yes because only 5 of the sample proportions were less than 15%. 5/100 = 5% which is low.

• No because 19/100 sample proportions gave a proportion of 15% or lower. 19% is not considered unusual.

• Yes because we should have gotten a sample proportion of 25% if that is actually the proportion of instant winners.