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- When the owner of a small business reviews her list of contracts for 2011, she finds that 35% of the contracts were from clients she met at a large conference at the end of 2010. Answer the following questions about this situation.
A. Was this measurement obtained by a sample or a census? What words in the description of the situation make you confident that your answer is correct? - Should the owner have taken into account some measure of reliability associated with the value 35%.
- An instructor wishes to review students doing poorly in his large-room lecture courses, so that he can schedule individual appointments with them and offer extra help. He has time to meet with only 15 students. That data in the table below lists student ID numbers and their current averages in the course. The professor asks you, as the teaching assistant, to answer the following questions:
- Create a Pareto chart showing the grades of the 15 students currently doing the worst.
- Report what percentage of the total range of grades is represented by the range of the 15 worst grades.
- A quality control analyst measures the number of hours a patient in a low-risk condition waits for car at the emergency room of a small hospital. The following data are obtained for 20 patients.
2.26 2.01 3.0 1.22 1.92 1.79 0.78 1.89 0.71 1.58
2.02 2.77 2.87 0.51 0.74 1.95 2.76 2.61 3.54 2.95
- Compute the sample mean, sample median, and range of data
- Compute the sample standard deviation and sample variance
- If the vertical axis of a graph is unusually tall, how might that misrepresent the data or mislead the viewer.
- A health inspector at a restaurant will enter the kitchen and choose 5 stations to
inspect from a predetermined list of 15 stations present in most restaurant kitchens.a. How many different sets of 5 stations exist? - If all sets are equally likely, what is the probability of each set?
- If the inspector were instead to randomly select 13 stations to inspect, how many
different sets of 13 stations would exist?
d. If all sets were equally likely, what is the probability of each set? - The company policy for customer service reps gives time off for positive reviews. If, in the first 20 calls a customer service agent handles in a day, 13 or more elect to take a subsequent survey and rate the service as “excellent” then the company gives the agent his or her final hour of work that day off, paid. Ellie receives excellent reviews from 30% of the calls in the first 7 hours of a workday, on what percentage of her 8 hour workdays does Ellie get the final hour off?
- Assume that the number of sales per day of an app in the Apple iOS App Store is normally distributed.
- What two parameters of the distribution would you need to be able to determine the probability of sales on a particular day exceeding 100 units?
- If the probability of sales exceeding 100 units is 20% and the mean daily sales is 86 units, then what is the standard deviation of the distribution?
- Since careful records have begun being kept in January, Eric's small business has delivered the following quantities of flowers throughout town.
| January | February | March | April | May | June | July | August | |
| Small Bouquets | 85 | 34 | 26 | 24 | 43 | 29 | 30 | 19 |
| Large Bouquets | 23 | 64 | 27 | 18 | 33 | 23 | 20 | 13 |
Assuming the data is normally distributed, construct two separate 90% confidence intervals, one for the number of deliveries of small bouquets in September and one for the number of large bouquets in September.
- Researchers are studying a new chemical process for producing dyes. Although they don’t know it, the yield of the process is normally distributed with µ = 550 kg and σ = 75 kg. The researchers plan to estimate the process’ mean yield by running the process 35 times, recording the yield each time. Have they chosen a large enough sample to be 90% confident that their computed mean will be within 20 kg of the actual mean? Show your work to justify your answer.
- 10. A quality control experiment is to be done on a machine that fills tubes with toothpaste. Its specifications require that it fill tubes with 4.7 oz. A random sample of 40 tubes filled by machine is taken and each tube is weighed. The resulting data are below, with the weight of the tube already having been subtracted from each. Perform a hypothesis test at the 90% confidence level to determine if the machine is performing according to specifications.66 4.61 4.71 4.63 4.70 4.62 4.63 4.61 4.70 4.56
4.60 4.66 4.68 4.57 4.67 4.72 4.67 4.64 4.66 4.75
4.69 4.64 4.67 4.65 4.69 4.65 4.75 4.53 4.57 4.74
4.68 4.67 4.66 4.68 4.64 4.65 4.64 4.80 4.71 4.69
