Goodtaste Ltd., a coffee manufacturer, has recently been prosecuted for selling an
underweight 100g jar of coffee. You have been asked to give assistance to the quality
control manager who is investigating the problem.
Jars are filled automatically and the filling machine can be preset to any desired
weight. For the 100g jars of coffee a weight of 101g is set. There is no subsequent
checking of the weight of individual jars , although samples are occasionally taken to
check for quality. The standard deviation will depend to a certain extent on the
weight, but for weights between 90g and 110g it is virtually constant at 1.5g.
You have been asked to apply your knowledge of the
problem. In particular you have been told that prosecution only occurs when the
product is underweight by more than 2%, so you need to find the probability that such
a weight could happen by chance.
(a) Assuming that the mean weight is 101g, what proportion of jars are:
(i) Under 100g in weight?
(ii) Under 98g in wieght?
(iii) Under 97g in weight?
(iv) Over 100g?
(b) What should the mean weight be set to in order that the probability of a jar
weighing less than 98g is less than 0.1%?
(c) Write a short note to the Quality Control Manager summarising your results.
Step by stepSolved in 4 steps
- A local college cafeteria has a self-service soft ice cream machine. The cafeteria provides bowls that can hold up to 16 ounces of ice cream. The food service manager is interested in comparing the average amount of ice cream dispensed by male students to the average amount dispensed by female students. A measurement device was placed on the ice cream machine to determine the amounts dispensed. Random samples of 85 male and 78 female students who got ice cream were selected. The sample averages were 7.23 and 6.49 ounces for the male and female students, respectively. Assume that the population standard deviations are 1.22 and 1.17 ounces, respectively. Using the 1% significance level, can you conclude that the average amount of ice cream dispensed by male college students is larger than the average amount dispensed by female college students? What is the type of test to be used?arrow_forwardYou want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable preliminary estimation for the population proportion. You would like to be 90% confident that you estimate is within 4% of the true population proportion. How large of a sample size is required?arrow_forwardYou want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable preliminary estimation for the population proportion. You would like to be 99% confident that you estimate is within 3% of the true population proportion. How large of a sample size is required?arrow_forward
- The control department of a light bulb manufacturer randomly picks 4400 light bulbs from the production lot every week. The records show that, when there is no malfunction, the defect rate in the manufacturing process (due to imperfections in the material used) is 1% . When 1.5% or more of the light bulbs in the sample of 4400 are defective, the control unit calls repair technicians for service. Answer the following. (If necessary, consult a list of formulas.) (a)Find the mean of p , where p is the proportion of defective light bulbs in a sample of 4400 when there is no malfunction. (b)Find the standard deviation of p . (c)Compute an approximation for P≥p0.015 , which is the probability that the service technicians will be called even though the system is functioning properly. Round your answer to four decimal places.arrow_forwardFor reasons of safety, a study of bears involved the collection of various measurements that were taken after the bears were anesthetized. When obtaining measurements from an anesthetized bear in the wild, it is relatively easy to use a tape measure to obtain the size of the chest, the length of the head, and the total length of the bear. It is difficult to find the weight because the bear must be lifted! Instead of actually weighing the bear, an estimate of the bears weight can be obtained from other measurements that were obtained. Use the data provided in cells E1 to H55 to answer the following questions. Head Length (HEADLEN) data is in cells E1 to E55. Length data is in cells F1 to F55. Chest size data is in cells G1 to G55. Weight data is in cells H1 to H55. All data sets have labels in first row. Develop the estimated regression equation that can be used to predict a bear's weight based on head length (HEADLEN), Length, and chest size. Place output in cell I1 Is the joint…arrow_forwardPlease help by providing detailed workings. Answers to a minimum of 6 d.p. Thanksarrow_forward
- Advil and Motrin IB produce the same headache relief medication with the active ingredient ibuprofen. Each pillshould contain 200 mg of ibuprofen. A health agency obtains a sample of ten tablets from both manufacturers and measureshow much ibuprofen each pill actually contains.Number of milligrams measuredAdvil 199.25 198.50 200.10 200.75 201.00 198.00 200.10 199.00 201.10 202.20Motrin IB 205.00 195.80 195.20 203.20 205.80 194.40 204.60 194.60 207.20 194.20(a) Verify on your calculator that each sample has a mean value of 200 mg.(b) What is the range of each sample?(c) However, based on the given sample values, which company would you prefer to buy from? Justify your answer with statisticalreasoning. (Hint: argue using standard deviation and explain why this is desirable in this situation)arrow_forwardYou want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable estimation for the population proportion. You would like to be 99.9% confident that you estimate is within 0.1% of the true population proportion. How large of a sample size is required?arrow_forwardWhat if PepsiCo wants to narrow their investigation to see if the ounces are specifically less than the listed amount. How would your hypothesis test change with these new circumstances?arrow_forward
- A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON