Exam 7: Sampling and Sampling Distributions

If random variable X is distributed according to a uniform distribution between 0 and 1 (X ~ U[0,1]),and you take a random sample of size 35,what is the probability that the sample mean will fall between 0.48 and 0.55?

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 inches and a standard deviation of 0.05 inch,the probability that Claude's sample has a mean greater than 120.0125 inches is _____________.

Suppose 40% of the population of pre-teens have a TV in their bedroom.If a random sample of 500 pre-teens is drawn from the population,then the probability that 44% or fewer of the pre-teens have a TV in their bedroom is _______.

A carload of palletized aluminum castings has arrived at Mansfield Motor Manufacturers. The car contains 1,000 pallets of 100 castings each. Mario Munoz,manager of Quality Assurance,directs the receiving crew to deliver the 127th and 869th pallets to his crew for 100% inspection. Mario randomly selected 127 and 869 from a table of random numbers. Mario's sample of 200 castings is a _____________.

Alice Zhong is the VP of operations at Pearl Financial Services.She wants to measure customer satisfaction after a new website and other changes were introduced a few months ago.28% of clients are from the healthcare industry,35% are manufacturing companies,27% are financial firms,and 7% are construction companies.For this purpose,she gets random five-digits numbers from the website random.org (which offers true random numbers on the Internet).Then she uses these numbers to select 140 random clients from the healthcare sector,175 from the manufacturing sector,135 from the manufacturing sector,and 35 from the construction sector.This is an example of ______.

Suppose the population of all public Universities shows the annual parking fee per student is $110 with a standard deviation of $18.If a random sample of size 49 is drawn from the population,the probability of drawing a sample with a sample mean between $100 and $115 is _______.

Suppose a population has a mean of 400 and a standard deviation of 24.If a random sample of size 144 is drawn from the population,the probability of drawing a sample with a mean less than 402 is _______.

A carload of steel rods has arrived at Cybermatic Construction Company. The car contains 1,000 bundles of 50 rods each. Claude Ong,manager of Quality Assurance,directs the receiving crew to deliver the 63rd and 458th bundles to his crew for 100% inspection. Claude randomly selected 63 and 458 from a table of random numbers. Claude's sample of 100 rods is a _____________.

If the population proportion is 0.90 and a sample of size 64 is taken,what is the probability that the sample proportion is more than 0.89?

Abel Alonzo,Director of Human Resources,is exploring employee absenteeism at the Harrison Haulers Plant. Abel knows that absenteeism varies significantly between departments. For example,workers in the wood shop are absent more than those in the tuning department and the size of the departments ranges from 40 to 120 workers. He orders a random sample of 10% of the workers from each of the six departments. Abel's sample is a ________________.

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 ___________.

Systematic sampling is a type of random sampling technique.

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 ________.

Financial analyst Larry Potts needs a sample of 100 securities listed on the New York Stock Exchange. In the current issue of the Wall Street Journal,2,531 securities are listed in the "New York Exchange Composite Transactions," an alphabetical listing of all securities traded on the previous business day. Larry uses a table of random numbers to select 100 numbers between 1 and 2,531. His sample is a ____________.

On Saturdays,cars arrive at David Zebda's Scrub and Shine Car Wash at the rate of 80 cars per hour during the ten-hour shift. David wants a sample of 40 Saturday customers to answer the long version of his quality service questionnaire. He instructs the Saturday crew to select the first 40 customers. His sample is a __________.

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 16 minutes is ________.

Financial analyst Larry Potts needs a sample of 100 securities listed on either the New York Stock Exchange (NYSE)or the American Stock Exchange (AMEX). According to the Wall Street Journal's "Stock Market Data Bank," 2,531 NYSE securities and AMEX 746 securities were traded on the previous business day. Larry directs his staff to randomly select 77 NYSE and 23 AMEX securities. His sample is a ____________.

Catherine Chao,Director of Marketing Research,needs a sample of Kansas City households to participate in the testing of a new toothpaste package. If 40% of the households in Kansas City prefer the new package,the probability that Catherine's random sample of 300 households will have a sample proportion greater than 0.45 is ___________.

The directory or map from which a sample is taken is called the census.

Suppose a population has a mean of 400 and a standard deviation of 24.If a random sample of size 144 is drawn from the population,the probability of drawing a sample with a mean between 395.5 and 404.5 is _______.