Exam 7: Sampling and Sampling Distributions

According to the central limit theorem,if a sample of size 81 is drawn from a population with a standard deviation of 72,the standard deviation of the distribution of the sample means would equal ___.

Albert Abbasi,VP of Operations at Ingleside International Bank,is evaluating the service level provided to walk-in customers.Accordingly,he plans a sample of waiting times for walk-in customers.If the population of waiting times has a mean of 15 minutes and a standard deviation of 4 minutes,the probability that Albert's sample of 64 will have a mean less than 15 minutes is ___.

Pinky Bauer,Chief Financial Officer of Harrison Haulers,Inc. ,suspects irregularities in the payroll system.If 10% of the 5,000 payroll vouchers issued since January 1,2000,have irregularities,the probability that Pinky's random sample of 200 vouchers will have a sample proportion of between .06 and .14 is ___.

Albert Abbasi,VP of Operations at Ingleside International Bank,is evaluating the service level provided to walk-in customers.Accordingly,he plans a sample of waiting times for walk-in customers.If the population of waiting times has a mean of 15 minutes and a standard deviation of 4 minutes,the probability that Albert's sample of 64 will have a mean less than 14 minutes is ___.

A carload of steel rods has arrived at Cybermatic Construction Company.The car contains 50,000 rods.Claude Ong,manager of Quality Assurance,directs his crew measure the lengths of 100 randomly selected rods.If the population of rods has a mean length of 120 centimetres and a standard deviation of 0.05 centimetres,the probability that Claude's sample has a mean greater than 120.0125 centimetres is ___.

Contrast sampling to census and differentiate among different methods of sampling,which include simple,stratified,systematic,and cluster random sampling;and convenience,judgment,quota,and snowball nonrandom sampling,by assessing the advantages associated with each.

Saving time and money are reasons to take a sample rather than do a census.

Systematic sampling is a type of nonrandom sampling technique.

Financial analyst Larry Potts needs a sample of 100 securities listed on the Toronto Stock Exchange.In the current issue of the Report on Business Magazine,2,531 securities are listed in the "Toronto Exchange Composite Transactions," an alphabetical listing of all securities traded on the previous business day.Larry randomly selects the 7th security as a starting point,and selects every 25th security thereafter (7,32,57,etc. ).His sample is a ___.

A population list,map,directory,or other source used to represent the population from which a sample is taken is called the census.

Suppose 30% of a population possess a given characteristic.If a random sample of size 1200 is drawn from the population,then the probability that less than 348 possess that characteristic is ___.

According to the central limit theorem,if a sample of size 64 is drawn from a population with a mean of 56,the mean of all sample means would equal ___.

Pinky Bauer,Chief Financial Officer of Harrison Haulers,Inc. ,suspects irregularities in the payroll system.She knows that 2,500 payroll vouchers have been issued since January 1,2000,and her staff doesn't have time to inspect each voucher.So,she orders her staff to inspect the last 200 vouchers.Her sample is a ___.

Describe the distribution of a sample's mean using the central limit theorem,correcting for a finite population if necessary.

According to the central limit theorem,for samples of size 64 drawn from a population with µ = 800 and σ = 56,the standard deviation of the sampling distribution of sample means would equal ___.

The central limit theorem states that if the sample size,n,is large enough (n ≥30),the distribution of the sample means is uniformly distributed regardless of the shape of the population.

If the population proportion is 0.90 and a sample of size 64 is taken,what is the probability that the sample proportion is less than 0.88?

Albert Abbasi,VP of Operations at Ingleside International Bank,is evaluating the service level provided to walk-in customers.Accordingly,he plans a sample of waiting times for walk-in customers.If the population of waiting times has a mean of 15 minutes and a standard deviation of 4 minutes,the probability that Albert's sample of 64 will have a mean between 13.5 and 16.5 minutes is ___.

A carload of steel rods has arrived at Cybermatic Construction Company.The car contains 50,000 rods.Claude Ong,manager of Quality Assurance,directs his crew measure the lengths of 100 randomly selected rods.If the population of rods has a mean length of 120 centimetres and a standard deviation of 0.05 centimetres,the probability that Claude's sample has a mean between 119.985 and 120.0125 centimetres is ___.

Suppose a population has a mean of 90 and a standard deviation of 28.If a random sample of size 49 is drawn from the population,the probability of drawing a sample with a mean between 80 and 100 is ___.