Exam 8: Sampling Distributions

Consider two population distributions labeled A and B. Distribution A is highly skewed and nonnormal, while distribution B is slightly skewed and near normal. In order for the sampling distributions of A and B to achieve the same degree of normality,

The sample standard deviation s is an unbiased estimator of the population standard deviation σ.

The standard deviation of all possible sample proportions increases as the sample size increases.

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 standard deviation of the sampling distribution of the sample mean.

A manufacturing company measures the weight of boxes before shipping them to the customers. If the box weights have a population mean and standard deviation of 90 lb and 24 lb, respectively, then based on a sample size of 36 boxes, what is the probability that the average weight of the boxes will be less than 84 lb?

In the upcoming election for governor, the most recent poll, based on 900 respondents, predicts that the incumbent will be reelected with 55 percent of the votes. From the 900 respondents, how many indicated that they would not vote for the current governor or indicated that they were undecided?

In a manufacturing process, a machine produces bolts that have an average length of 3 inches with a variance of .03. If we randomly select three bolts from this process, what is the probability the mean length of the bolt is at most 3.1 inches?

Suppose that 60 percent of the voters in a particular region support a candidate. Find the probability that a sample of 1,000 voters would yield a sample proportion in favor of the candidate within 2 percentage points.

There is no easy way to calculate an unbiased point estimate of σ.

Find P( > 172), if μ = 175 and = 9.

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. What is the probability that fewer than 64 patients will not be satisfied with the after-surgery care?

________ says that if the sample size is sufficiently large, then the sample means are approximately normally distributed.

A golf tournament organizer is attempting to determine whether hole (pin) placement has a significant impact on the average number of strokes for the 13th hole on a given golf course. Historically, the pin has been placed in the front right corner of the green and the historical mean number of strokes for the hole has been 4.25, with a standard deviation of 1.6 strokes. On a particular day during the most recent golf tournament, the organizer placed the hole (pin) in the back left corner of the green. Sixty-four golfers played the hole with the new placement on that day. Determine the probability of the sample average number of strokes exceeding 4.75 using the historical mean and standard deviation.

A random sample of size 1,000 is taken from a population where p = .20. What is ?

The chief chemist for a major gasoline production company claims that the regular unleaded gasoline produced by the company contains on average 4 ounces of a certain ingredient. The chemist further states that the distribution of this ingredient per gallon of regular unleaded gasoline is normal and has a standard deviation of 1.2 ounces. What is the probability of finding an average in excess of 4.3 ounces of this certain ingredient from 100 randomly inspected 1-gallon samples of regular unleaded gasoline?

The chief chemist for a major gasoline production company claims that the regular unleaded gasoline produced by the company contains on average 4 ounces of a certain ingredient. The chemist further states that the distribution of this ingredient per gallon of regular unleaded gasoline is normal and has a standard deviation of 1.2 ounces. What is the probability of finding an average of less than 3.85 ounces of this certain ingredient from 64 randomly inspected 1-gallon samples of regular unleaded gasoline?

The population of all ________ proportions is described by the sampling distribution of .

A research study investigated differences between male and female students. Based on the study results, we can assume the population mean and standard deviation for the GPA of male students are µ = 3.5 and σ = .5. Suppose a random sample of 100 male students is selected and the GPA for each student is calculated. What is the probability that the random sample of 100 male students has a mean GPA greater than 3.42?

In a manufacturing process, a machine produces bolts that have an average length of 3 inches with a variance of .03. If we randomly select three bolts from this process, what is the standard deviation of the sampling distribution of the sample mean?

Suppose that 60 percent of the voters in a particular region support a candidate. Find the probability that a sample of 1,000 voters would yield a sample proportion in favor of the candidate within 4 percentage points of the actual proportion.