A bolt fabrication machine makes bolts with a target length of = 15.125 millimeters. The machine has some variability, so the standard deviation of the length is = 0.175 millimeter. The machine operator inspects a random sample of 12 bolts each hour for quality control purposes and records the sample mean diameter, x. Assuming the process is working properly, what are the mean and standard deviation of the sampling distribution of x?

x= 15.125 and x= 0.175

x= 12 and x= 0.175

x= 12 and x= 0.0505

x= 15.125 and x= 3.46

x= 15.125 and x= 0.0505

Suppose we select a simple random sample of size n = 125 from a large population with a proportion p of successes. Letpbe the proportion of successes in the sample. For which value of p is it appropriate to use the Normal approximation for the sampling distribution ofp?

0.03

0.02

0.97

0.94

0.25

A city is interested in building a swan sanctuary in a certain area. One hundred fifty randomly selected residents from this area were asked, "Do you support the city's decision to build a swan sanctuary in your area?" Of the 150 residents interviewed, 76 said no, 9 said yes, and 65 had no opinion. A large-sample z-confidence interval,p z * sqrt of p(1-p)/n, was constructed from these data to estimate the proportion of the residents who support building a swan sanctuary in a certain area. Which of the following statements is correct for this confidence interval?

This confidence interval is valid because a sample size of more than 30 was used.

This confidence interval is valid because each area resident was asked the same question.

The confidence interval is valid because no conditions are required for constructing a large-sample confidence interval for a proportion.

This confidence interval is not valid because "no opinion" was included as a response category for the question.

This confidence interval is not valid because the quantity npis too small.

A zoning board in Pine County is interested in estimating the proportion of its residents in favor of larger school zones in that county. A random sample of Pine County residents was selected. All the selected residents were asked, "Are you in favor of larger school zones in your county?" A 95% confidence interval for the proportion of residents in favor of larger school zones in that county was calculated to be 0.48 0.02. Which of the following statements is correct?

At the 95% confidence level, the majority of area residents is in favor of larger school zones in that county.

In repeated sampling, 95% of sample proportions will fall in the interval (0.46, 0.50).

At the 95% confidence level, the estimate of 0.48 is within 0.02 of the true proportion of county residents in favor of larger school zones in that county.

In repeated sampling, the true proportion of county residents in favor of larger school zones in that county will fall in the interval (0.46, 0.50).

In repeated sampling, 95% of the time, the true proportion of county residents in favor of larger school zones in that county will be equal to 0.48.