Exam 8: Sampling Distributions

Packages of sugar bags for Sweeter Sugar Inc. have an average weight of 16 ounces and a standard deviation of .3 ounces. The weights of the sugar packages are normally distributed. What is the probability that 9 randomly selected packages will have an average weight in excess of 16.025 ounces?

If the sampled population is finite and at least ________ times larger than the sample size, we treat the population as infinite.

Packages of sugar bags for Sweeter Sugar Inc. have an average weight of 16 ounces and a standard deviation of .2 ounces. The weights of the sugar packages are normally distributed. What is the probability that 16 randomly selected packages will have a weight in excess of 16.075 ounces?

If p = .8 and n = 50, then we can conclude that the sampling distribution of is approximately a normal distribution.

It has been reported that the average time to download the home page from a government website was .9 seconds. Suppose that the download times were normally distributed with a standard deviation of .3 seconds. If random samples of 36 download times are selected, 80 percent of the sample means will be between what two values symmetrically distributed around the population mean?

A random sample of size 1,000 is taken from a population where p = .20. Find P( < .18).

The internal auditing staff of a local manufacturing company performs a sample audit each quarter to estimate the proportion of accounts that are more than 90 days overdue (delinquent). The historical records of the company show that over the past 8 years, the average has been that 13 percent of the accounts have been delinquent. For this quarter, the auditing staff randomly selected 250 customer accounts. What is the probability that no more than 40 accounts will be classified as delinquent?

It has been reported that the average time to download the home page from a government website was .9 seconds. Suppose that the download times were normally distributed with a standard deviation of .3 seconds. If random samples of 36 download times are selected, calculate the mean of the sampling distribution of the sampling mean.

The standard deviation of the sampling distribution of the sample mean is σ.

The mean of the sampling distribution of is always equal to the mean of the sampled population.

The number of defectives in 10 different samples of 50 observations each is the following: 5, 1, 1, 2, 3, 3, 1, 4, 2, 3. What is the estimate of the population proportion of defectives?

A random sample of size 1,000 is taken from a population where p = .20. Find P( > .175).

According to a hospital administrator, historical records over the past 10 years have shown that 20 percent of the major surgery patients are dissatisfied with after-surgery care in the hospital. A scientific poll based on 400 hospital patients was conducted and 64 patients indicated that they were dissatisfied with the after-surgery care. What are the mean and the standard deviation of the sampling distribution of ?

A random sample of size 1,000 is taken from a population where p = .20. Describe the sampling distribution of .

The mean of the sampling distribution of the sample proportion is equal to ________ when the sample size is sufficiently large.

A theorem that allows us to use the normal probability distribution to approximate the sampling distribution of sample means and sample proportions whenever the sample size is large is known as ________.

If a population is known to be normally distributed, then the sample standard deviation must equal σ.

A random sample of size 36 is taken from a population with mean 50 and standard deviation 5. Find P( > 49).

If the sampled population is exactly normally distributed, then the sampling distribution of is also expected to be normal, regardless of the sample size.

The diameter of small Nerf balls manufactured overseas is expected to be approximately normally distributed with a mean of 5.2 inches and a standard deviation of .08 inches. Suppose a random sample of 20 balls is selected. Calculate the standard deviation of the sampling distribution of the sample mean.