Exam 7: Introduction to Sampling Distributions

If a population is normally distributed, then the sampling distribution for the sample mean will always be normally distributed regardless of the sample size.

The makers of a particular type of candy have stated that 75 percent of their sacks of candy will contain 6 ounces or more of candy. A consumer group that studies such claims recently selected a random sample of 100 sacks of this candy. Of these, 70 sacks actually contained 6 ounces or more. The probability that 70 or fewer sacks would contain 6 ounces or less is approximately 0.1251.

The monthly electrical utility bills of all customers for the Far East Power and Light Company are known to be distributed as a normal distribution with mean equal to $87.00 a month and standard deviation of $36.00. If a statistical sample of n = 100 customers is selected at random, what is the probability that the mean bill for those sampled will exceed $75.00?

According to the local real estate board, the average number of days that homes stay on the market before selling is 78.4 with a standard deviation equal to 11 days. A prospective seller selected a random sample of 36 homes from the multiple listing service. Above what value for the sample mean should 95 percent of all possible sample means fall?

A major automobile manufacturer has developed a new model car that it claims will average 25 mpg on the highway. A random sample of fifty of these cars was tested and they averaged 24 mpg. This means that the claim made by the auto company is incorrect.

The annual income for independent sales representatives in the United States is thought to be highly right-skewed with a mean equal to $144,300 and a standard deviation of $32,450. Given this information, if a sample of 36 independent sales representatives is selected, what is the probability that the mean of the sample will exceed $130,000?

A sampling distribution for a sample mean shows the distribution of the possible values for the sample mean for a given sample size from a population.

A local bank has 1,400 checking account customers. Of these, 1,020 also have savings accounts. A sample of 400 checking account customers was selected from the bank of which 302 also had savings accounts. The sampling error in this situation is .0264.

The following values represent the population of home mortgage interest rates (in percents) being charged by the banks in a particular city: Given this information, what is the smallest amount of sampling error possible if a random sample of n = 3 banks is surveyed and the mean loan rate is calculated?

The actual mean fill volume for all bottles of a soft drink product that were filled on a Tuesday is 11.998 ounces. A sample of 64 bottles was randomly selected and the sample mean fill volume was 12.004 ounces. Based upon this information, the sampling error is .006 ounce.

Suppose it is known that the ages of all employees working for a very large computer company is normally distributed with a mean of 44.2 and a standard deviation of 5.6 years. Given this information, discuss what the sampling distribution for looks like?

If the mean age for all students that attend your university is 24.78 years, it would be reasonable to expect that the mean of a sample of students selected from that population would also equal 24.78 years as long at the sampling is done using sound statistical methods.

Princess Cruises recently offered a 16-day voyage from Beijing to Bangkok during the time period from May to August. The announced price, excluding airfare, for a room with an ocean view or a balcony was listed as $3,475. Cruise fares usually are quite variable due to discounting by the cruise line and travel agents. A sample of 20 passengers who purchased this cruise paid the following amounts (in dollars): Determine the sampling error for this sample.

The St. Joe Company grows pine trees and the average annual increase in tree diameter is 3.1 inches with a standard deviation of 0.5 inch. A random sample of n = 50 trees is collected. What is the probability of the sample mean being less the 2.9 inches?

A population has a proportion equal to 0.30. Calculate the following probabilities with n = 100. Find

Explain the impact of the size of the sample on the shape of the sampling distribution.

The population of incomes in a particular community is thought to be highly right-skewed with a mean equal to $36,789 and a standard deviation equal to $2,490. Based on this, if a sample of size n = 36 is selected, the highest sample mean that we would expect to see would be approximately $38,034.

The Olsen Agricultural Company has determined that the weight of hay bales is normally distributed with a mean equal to 80 pounds and a standard deviation equal to 8 pounds. Based on this, what is the probability that the mean weight of the bales in a sample of n = 64 bales will be between 78 and 82 pounds?

The Central Limit Theorem is of most use to decision makers when the population is known to be normally distributed.

Suppose nine items are randomly sampled from a normally distributed population with a mean of 100 and a standard deviation of 20. The nine randomly sampled values are: Calculate the probability of getting a sample mean that is smaller than the sample mean for these nine sampled values.