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- Use Excels functions (not @RISK) to generate 1000 random numbers from a normal distribution with mean 100 and standard deviation 10. Then freeze these random numbers. a. Calculate the mean and standard deviation of these random numbers. Are they approximately what you would expect? b. What fraction of these random numbers are within k standard deviations of the mean? Answer for k = 1; for k = 2; for k = 3. Are the answers close to what they should be (about 68% for k = 1, about 95% for k = 2, and over 99% for k = 3)? c. Create a histogram of the random numbers using about 10 bins of your choice. Does this histogram have approximately the shape you would expect?4.1 TYPES OF RANDOM VARIABLES. Which of the following describe continuous random variables? Which describe discrete random variables? The number of newspapers sold by the New York Times each month The amount of ink used in printing a Sunday edition of the New York Times The actual number of ounces in a 1-gallon bottle of laundry detergent The number of defective parts in a shipment of nuts and bolts The number of people collecting unemployment insurance each monthBill Kime's bowling ball factory makes bowling balls of adult size and weight only. The standard deviation in the weight of a bowling ball produced at the factory is known to be 0.39 pounds. Each day for 24 days, the average weight, in pounds, of 9 of the bowling balls produced that day has been assessed as follows Day 1 2 3 4 5 6 Average (lb) 9.9 9.9 10.1 10.1 99 99 Day 7 8 9 10 11 12 Average (lb) Day Average (b) 13 14 15 16 17 18 10.1 10.0 10.0 10.1 10.1 10.0 9.9 10.1 10.1 10.0 10.1 10.1 Day 19 20 21 22 23 24 Average (lb) 99 10.0 10.1 9.9 10.0 10.0 a) Establish a control chart for monitoring the average weights of the bowling balls in which the upper and lower control limits are each two standard deviations from the mean What are the values of the control limits? Upper Control Limit (UCL)=b (Round your response to two decimal places)
- According to Reader's Digest, 47% of primary care doctors think their patients receive unnecessary medical care. Use z-table. a. Suppose a sample of 310 primary care doctors was taken. Show the sampling distribution of the proportion of the doctors who think their patients receive unnecessary medical care. E(F) (to 4 decimals) b. What is the probability that the sample proportion will be within ±0.03 of the population proportion. Round your answer to four decimals. c. What is the probability that the sample proportion will be within 0.05 of the population proportion. Round your answer to four decimals. d. What would be the effect of taking a larger sample on the probabilities in parts (b) and (c)? Why? The probabilities would - Select your answer - This is because the increase in the sample size makes the standard error, Op . - Select your answer - ♥Elon Corporation manufactures parts for an aircraft com-pany. It uses a computerized numerical controlled (CNC) machining center to produce a specific part that has adesign (nominal) target of 1.275 inches with tolerancesof 0.024 inch. The CNC process that manufacturesthese parts has a mean of 1.281 inches and a standarddeviation of 0.008 inch. Compute the process capabilityratio and process capability index, and comment onthe overall capability of the process to meet the designspecifications.An industrial process that makes 3-foot sections of plasticpipe produces pipe with an average inside diameter of 1 inch and a standard deviation of .05 inch.a. If you randomly select one piece of pipe, what is the probability that its inside diameter willexceed 1.02 inches, assuming the population is normal?b. If you select a random sample of 25 pieces of pipe, what is the probability that the sample meanwill exceed 1.02 inches?μ = 1.00, σ = .05
- Elon Corporation manufactures parts for an aircraft company. It uses a computerized numerical controlled (CNC) machining center to produce a specific part that has a design (nominal) target of 1.275 inches with tolerances of ±0.024 inch. The CNC process that manufactures these parts has a mean of 1.281 inches and a standard deviation of 0.008 inch. Which of the following statements is true concerning the process capability ratio and process capability index? O The process is off center and incapable. O The process is centered, but incapable. The process is capable and centered. O The process is capable, but off center.What is the meaning of x ~ N (50, 20)? 1. Sampling distribution of x is distributed with a mean of 20 and a standard deviation of 50 2. x-bar is normally distributed with a mean of 20 and a standard deviation of 50 3. x is normally distributed with a mean of 50 and a standard deviation of 20 4. Sampling distribution of x is distributed with a mean of 50 and a standard deviation of 20What is the meaning of x ̅ ~ N (50, 2)? 1. The Sampling distribution is distributed normally with a mean of 50 and a standard deviation of 2 2. Sampling distribution of x is distributed normally with a mean of 2 and a standard deviation of 50 3. x is normally distributed with a mean of 50 and a standard deviation of 2 4. x-bar is normally distributed with a mean of 2 and a standard deviation of 50
- A researcher is studying whether being a smoker causes people to get colds more often. Classify each method as a survey, an experiment, or an observational study. Then explain which method would be the most reliable. Method A: Choose people who already smoke and who do not and monitor how many colds they get in a period of years. Method B: Choose 100 people at random. Have 50 people smoke regularly for six months and 50 people not smoke for six months. Then monitor how many of the 100 people get colds within the next six months. Method C: Ask people who currently have a cold whether or not they smoke. Tell whether each method of gathering data is a survey, an observational study, or an experiment. Which option would give the most reliable results?The director of research and development is testing a new drug. She wants to know if there is evidence at the 0.05 level that the drug stays in the system for more than 399 minutes. For a sample of 81 patients, the mean time the drug stayed in the system was 401 minutes. Assume the standard deviation is known to be 21. Step 1 of 5: Enter the hypotheses: Step 2 of 5: Enter the value of the z test statistic. Round your answer to two decimal places. Step 3 of 5: Specify if the test is one-tailed or two-tailed. Step 4 of 5: Enter the decision rule. Step 5 of 5: Enter the conclusion.4. ABC Dog Food Company located in Ottawa sells large bags of dog food to warehouse clubs. ABC uses an automatic filling process to fill the bags. Weights of the filled bags are approximately normally distributed with a mean of 50 kilograms and a standard deviation of 1.25 kilograms. (a) What is the probability that a filled bag will weigh less than 49.5 kilograms? (b) What is the probability that a randomly sampled filled bag will weigh between 48.5 and 51 kilograms? (c) What is the minimum weight a bag of dog food could be and remain in the top 15% of all bags filled? (d) ABC is unable to adjust the mean of the filling process. However, it is able to adjust the standard deviation of the filling process. What would the standard deviation need to be so that 2% of all filled bags weigh more than 52 kilograms?