Exam 5: Sampling Distributions

The number of undergraduates at Johns Hopkins University is approximately 2000,while the number at Ohio State University is approximately 40,000.Suppose the actual proportion of undergraduates at Johns Hopkins University who feel drinking is a problem among college students is 67%.A simple random sample of 50 undergraduates at Johns Hopkins University found that 60% of those sampled felt that drinking was a problem among college students.Which value(s)can be labeled as a parameter(s)?

For the following scenario,determine if the numbers in boldface type are statistics or parameters. A company manufactures cardboard containers for packaging frozen fruit juices.The manufacturing process forms the containers by joining cardboard stock to a metal bottom.The container can be inspected to determine if there might be leaks along the cardboard seam or where the metal bottom is attached.It is known from long experience that 18% of cans produced by this process are defective.A random sample of 50 cans was selected from the production process on Monday,and it was found that 12% of the selected cans were defective.Because this seemed to indicate an improvement,another sample was selected of the same size on Tuesday,and in it 21% of the cans were defective.The numbers 12%,18%,and 21% are,respectively,a

Thousands of batteries are produced every day in a certain manufacturing plant.The quality control specialist is interested in how long it takes for each battery to fail when used in a moderately sized appliance,like a portable radio or CD player.The quality control specialist will take a simple random sample of 2000 batteries produced at this plant over the next four days.These batteries will be put into a variety of moderately sized appliances and the average of all failure times will be computed.Which of the following probability distributions is most appropriate to model the average time until failure of these 2000 batteries?

Chocolate bars produced by a certain machine are labeled 8.0 ounces.The distribution of the actual weights of these chocolate bars is claimed to be Normal with a mean of 8.1 ounces and a standard deviation of 0.1 ounces.If the quality control manager takes a simple random sample of 10 chocolate bars from the production line,what is the probability that the sample mean weight of the 10 sampled chocolate bars will be less than 8.0 ounces?

A random variable X is Normally distributed with mean = 75 and = 8.Let Y be a second Normally distributed random variable with mean = 70 and = 12.It is also known that X and Y are independent of one another.Let W be a random variable that is the difference between X and Y (i.e. ,W = X - Y).What is the probability that W is greater than -5.5 (i.e. ,P{W > -5.5})?

A study,conducted by Jackson et al.and published in the journal Cancer Causes and Control in 2009,examined 33,938 women aged 40 to 84 years old who resided in California and who reported having had a mammogram within the last 2 years.The researchers were interested in characteristics of women who routinely obtain mammograms,as suggested by the American Cancer Society,to detect breast cancer.The table below provides a column that refers to the sample size and provides characteristics of the 33,938 women who were included in the study who reported having had a mammogram. Having such a low number of the respondents being African American would create _____ variability in their responses.

Chocolate bars produced by a certain machine are labeled 8.0 ounces.The distribution of the actual weights of these chocolate bars is claimed to be Normal with a mean of 8.1 ounces and a standard deviation of 0.1 ounces.The quality control manager plans to take a simple random sample of size n from the production line.How big should n be so that the sampling distribution of has a standard deviation of 0.01 ounces?

The weights of extra-large eggs have a Normal distribution with a mean of 1 ounces and a standard deviation of 0.1 ounces.What is the probability that a carton of a dozen eggs weighs more than 13 ounces?

A length of chain is to be constructed by placing 36 component links end to end.The length of a link produced by a production process is known to be a random variable with a mean of  = 2.5 centimeters and a standard deviation of  = 0.2 centimeters.The 36 links are chosen at random from this process to produce the chain.The mean and standard deviation of the length of chain are,respectively,_________.

A gasoline tank for a certain car is designed to hold 15 gallons of gas.Suppose that the actual capacity of a randomly selected tank has a distribution that is approximately Normal with a mean of 15.0 gallons and a standard deviation of 0.15 gallons.What proportion of tanks will hold between 14.75 and 15.10 gallons of gas?

Chocolate bars produced by a certain machine are labeled 8.0 ounces.The distribution of the actual weights of these chocolate bars is claimed to be Normal with a mean of 8.1 ounces and a standard deviation of 0.1 ounces.A quality control manager initially plans to take a simple random sample of size n from the production line.If he were to double his sample size (to 2n),by what factor would the standard deviation of the sampling distribution of change?

The length of time it takes to get through the security checks at a very large urban airport is a random variable with a mean of  = 20.6 minutes and a standard deviation of  = 8.4 minutes.A simple random sample of 36 airline passengers is to be observed going through security.What is the mean of the sampling distribution of the sample mean ?

Thousands of batteries are produced every day in a certain manufacturing plant.The quality control specialist is interested in how long it takes for each battery to fail when used in a moderately sized appliance,like a portable radio or CD player.Which of the following probability distributions is most appropriate to model the time until failure of these batteries?

Consider a Poisson distribution with a mean of 4.What is the probability that X < 3?

A study,conducted by Jackson et al.and published in the journal Cancer Causes and Control in 2009,examined 33,938 women aged 40 to 84 years old who resided in California and who reported having had a mammogram within the last 2 years.The researchers were interested in characteristics of women who routinely obtain mammograms,as suggested by the American Cancer Society,to detect breast cancer.The table below provides a column that refers to the sample size and provides characteristics of the 33,938 women who were included in the study who reported having had a mammogram. The margin of error for the white respondents is likely _____ the African American respondents.

Suppose a simple random sample is selected from a population with a mean if  and a variance of ².The central limit theorem tells us that

The weights of extra-large eggs have a Normal distribution with a mean of 1 ounces and a standard deviation of 0.1 ounces.What is the sampling distribution of the sample mean weight of the eggs in a randomly selected carton of a dozen eggs?