# Estimation

The Greensboro Coliseum is considering expanding its searing capacity and needs to know both the average number of people who attend events there and the variability in this number. The following are the attendances (in thousands) at nine randomly selected sporting events. Find point estimates of the mean and the variance of the population from which the sample was drawn.

 8.8 14 21.3 7.9 12.5 20.6 16.3 14.1 13

The Pizza Distribution Authority (PDA) has developed quite a business in Carrboro by delivering pizza orders promptly. PDA guarantees that its pizzas will be delivered in 30 minutes or less from the time the order was placed, and if the delivery is late, the pizza is free. The time that it takes to deliver each pizza order that is on time is recorded in the Official Pizza Time Book (OPTB), and the delivery time for those pizzas that are delivered late is recorded as 30 minutes in the OPTB. Twelve random entries from the OPTB are listed.

 15.3 29.5 30 10.1 30 19.6 10.8 12.2 14.8 30 22.1 18.3
1. Find the mean for the sample.
3. Can this sample be used to estimate the average time that it takes for PDA to deliver a pizza? Explain.

Joe Jackson, a meteorologist for local television station WDUL, would like to report the average rainfall for today on this evening's newscast.

 8.8 14 21.3 7.9 12.5 20.6 16.3 14.1 13

The National Bank of Lincoln is trying to determine the number of tellers available during the lunch rush on Fridays. The bank has collected data on the number of people who entered the bank during the last 3 months on Friday from 11 A.M. to 1 P.M. Using the data below, find point estimates of the mean and standard deviation of the population from which the sample was drawn.

 242 275 289 306 242 385 279 245 269 305 294 328

Electric Pizza was considering national distribution of its regionally successful product and was compiling pro forma sales data. The average monthly sales figures (in thousands of dollars) from its 30 current distributors are listed. Treating them as (a) a sample and (b) a population, compute the standard deviation.

 7.3 5.8 4.5 8.5 5.2 4.1 2.8 3.8 6.5 3.4 9.8 6.5 6.7 7.7 5.8 6.8 8 3.9 6.9 3.7 6.6 7.5 8.7 6.9 2.1 5 7.5 5.8 6.4 5.2

In a sample of 400 textile workers, 184 expressed extreme dissatisfaction regarding a prospective plan to modify working conditions. Because this dissatisfaction was strong enough to allow management to interpret plan reaction as being highly negative, they were curious about the proportion of total workers harboring this sentiment. Give a point estimate of this proportion

The Friends of the Psychics network charges \$3 per minute to learn the secrets that can turn your life around. The network charges for whole minutes only and rounds up to benefi t the company. Thus, a 2 minute 10 second call costs \$9. Below is a list of 15 randomly selected charges.

 3 9 15 21 42 30 6 9 6 15 21 24 32 9 12
1. Find the mean of the sample.
2. Find a point estimate of the variance of the population.
3. Can this sample be used to estimate the average length of a call? If so, what is your estimate? If not, what can we estimate using this sample?

For a population with a known variance of 185, a sample of 64 individuals leads to 217 as an estimate of the mean.

1. Find the standard error of the mean.
2. Establish an interval estimate that should include the population mean 68.3 percent of the time.

Eunice Gunterwal is a frugal undergraduate at State U. Who is interested in purchasing a used car. She randomly selected 125 want ads and found that the average price of a car in this sample was \$3,250. Eunice knows that the standard deviation of used-car prices in this city is \$615

1. Establish an interval estimate for the average price of a car so that Eunice can be 68.3 percent certain that the population mean lies within this interval.
2. Establish an interval estimate for the average price of a car so that Miss Gunterwal can be 95.5 percent certain that the population mean lies within this interval.

From a population known to have a standard deviation of 1.4, a sample of 60 individuals is taken. The mean for this sample is found to be 6.2.

1. Find the standard error of the mean.
2. Establish an interval estimate around the sample mean, using one standard error of the mean.