Exam 7: Continuous Probabilitydistributions

GreenFacts, a non-profit organization, reports that the average adult in Europe consumed 17 litres of Alcohol last year. The standard deviation is 2.1 litres. If we randomly select 42 European adults, what Is the probability that the sample mean is more than 17.8 litres?

(i. The type of sampling when a population is first divided into subgroups and then a sample is Selected from each subgroup is called random sampling. (ii. Auditors may select every 20th file starting with say, the 5th file in the top drawer. Then file Numbers 25, 45, 65, 85,... are audited. This type of sampling is called systematic sampling. (iii) The mean of a population is called a parameter.

(i. The standard error of the mean is the standard deviation of the sampling distribution of the Sample means. (ii. The standard deviation of the sampling distribution of the mean is always smaller than the Standard deviation of the population under study. (iii) For a sampling distribution of the means, 95% of the means would be between ± 1.96 standard Deviations.

An experiment involves selecting a random sample of 256 middle managers at random for study. One item of interest is their mean annual income. The sample mean is computed to be $35,420 and The sample standard deviation is $2,050. What is the standard error of the mean?

We wish to study the advertising expenditures for the 200 largest companies in Canada. Suppose The objective of the study is to determine whether firms with high returns on equity (a measure of Profitability) spent more of each sales dollar on advertising than firms with a low return or deficit. To Make sure that the sample is a fair representation of the 200 companies, the companies are Grouped on percent return on equity What is this type of sampling called?

(i. The standard error of the mean is the standard deviation of the sampling distribution of the Sample means. (ii. The standard deviation of the sampling distribution of the mean is always smaller than the Standard deviation of the population under study. (iii) For a sampling distribution of the means, 90% of the means would be between ± 1.96 standard Deviations.

(i. The standard error of the mean is the standard deviation of the sampling distribution of the Sample means. (ii. The standard deviation of the sampling distribution of the mean is always larger than the Standard deviation of the population under study. (iii) For a sampling distribution of the means, 95% of the means would be between ± 1.96 standard Deviations.

The mean of all possible sample means is equal to the

An accounting firm is planning for the next tax preparation season. From last year's returns, the firm Collects a systematic random sample of 100 filings. The 100 filings showed an average preparation Time of 90 minutes with a standard deviation of 140 minutes. What is the probability that a sample mean would exceed 90 minutes per filing?

The mean weight of trucks traveling on a particular section of I-475 is not known. A provincial Highway inspector needs an estimate of the mean. He selects a random sample of 49 trucks Passing the weighing station and finds the mean is 15.8 tonnes, with a standard deviation of the Sample of 4.2 tonnes. What is probability that a truck will weigh less than 14.3 tonnes?

What sample statistic is used to estimate a population parameter?

Dawson's Repair Service orders parts from an electronic company who advertises its parts o be no More than 2% defective. What is the probability that Bill Dawson finds 2 or more parts out of a Sample of 60 to be defective?

What is it called when all the items in a population have a chance of being selected in a sample?

Manufacturers were subdivided into groups by volume of sales. Those with more than $100 million In sales were classified as Class A large; those from $50 to $100 million as Class A medium size; And those between $25 and $50 million, and so on. Samples were then selected from each of These groups. What is this type of sampling called?

i. A simple random sample assumes that each item or person in the population has an equal chance Of being included. ii. We can expect some difference between sample statistics and the corresponding population Parameters. This difference is called the sampling error. iii. A sampling distribution of the means is a probability distribution consisting of a list of all possible Sample means of a given sample size selected from a population and the probability of occurrence Associated with each sample mean.

Suppose a research firm conducted a survey to determine the average amount of money steady Smokers spend on cigarettes during a week. A sample of 100 steady smokers revealed that the Sample mean is $20 and the sample standard deviation is $5. What is the probability that a sample Of 100 steady smokers spend between $19 and $21?

i. If probability sampling is done, each item in the population has a chance of being chosen. ii. If the size of a sample equals the size of the population, we would not expect any error in Estimating the population parameter.

Alpha Corporation receives a shipment of flour every morning from their supplier. The flour is in 40 Kg bags and Alpha will reject any shipment that is more than 5% underweight. The foreman samples 60 bags with each shipment and if the bags average more than 5% underweight, the whole Shipment is returned to the supplier. Determine the value for the standard error of the proportion.

Mileage tests were conducted on a randomly selected sample of 100 newly developed automobile Tires. The average tread wear was found to be 50,000 miles with a standard deviation of 3,500 Miles. What is the best estimate of the average tread life in miles for the entire population of these Tires?

An accounting firm is planning for the next tax preparation season. From last year's returns, the firm Collects a systematic random sample of 100 filings. The 100 filings showed an average preparation Time of 90 minutes with a standard deviation of 140 minutes. What is the probability that average preparation time is between 80 and 90 minutes?