Given a normal distribution with μ= 105 and σ = 20, and given you select a sample of n = 16, complete parts (a) through (d). a. What is the probability that X is less than 92? P(X<92) 0.0047 (Type an integer or decimal rounded to four decimal places as needed.) b. What is the probability that X is between 92 and 93.5? P(92 X 93.5)= 0.0061 (Type an integer or decimal rounded to four decimal places as needed.) c. What is the probability that X is above 105.2? P(X 105.2)= 0.4840 (Type an integer or decimal rounded to four decimal places as needed.) d. There is a 67% chance that X is above what value? X = (Type an integer or decimal rounded to two decimal places as needed.)
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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?Bill 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)(29) Please calculate the standard deviation for the following. Please round to 2 decimals (if answer is 10% please answer 10.00) State of nature Eret A B C D 5.50% 8% -2% 3.60% Probability 14% ? 31% 48%
- What 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 50calculate x-bar for the data shown, to two decimal places, 9,7.9,10,21.8,7A single sampling inspection scheme for large lot of mass-produced flanges states:From each lot take and inspect a random sample of 50. If 3 or more defectives, inspect the whole lot and remove all defectives, if less than 3 are found accept the lot without further inspection.a. Obtain the equation for Pa the probability that a lot containing a fraction p of defectives will be accepted, in terms of p.b. Evaluate Pa for p=0.01, 0.02, 0.03, 0.05, 0.07, 0.10, 0.15, 0.20, 0.30. Plotthe operating characteristics and average outgoing quality curve.c. Estimate: (a) the producer’s Risk at p of 2% (b) the consumer’s Risk for pof 5%.
- 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 month5. Construct the frequency distribution for the data. For calculating the cell width assume 7 cells, the lower limit of 25.35 inches and upper limit of 25.42 inches. Round your answers for interval boundaries to three decimal places and round your answers for frequencies to the nearest whole number. Cell From To (inclusive) Frequency 09 25.360 X 1 7 2 3 456 10 a 8 9 10 10 KWhat 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 20
- 1. Statistical process control, hypothesis testing, and control charts Consumers value prompt service when they order takeout or delivered pizza, and pizza restaurants compete for customers by making time promises. Papa John's, for instance, offers a 10-minute takeout guarantee. Domino's advertises a 30-minute delivery time. Suppose that the quality control manager at a nationwide pizza chain defines this production variable: An order is processed on time or late. Every night, a random sample of pizza orders is selected, and data are collected on the production variable for each order in the sample. To detect a change in the number of orders that are late, the quality control manager uses Based on the control chart, the quality control manager decides that the variation in output is due to assignable causes. Consequently, the manager concludes that the production process is ; it is Statistical procedures for process control use a hypothesis-testing framework. The null and alternative…Suppose you sample one value from a uniform distribution with a = 0 and b=20. a. What is the probability that the value will be between 12 and 172 b. What is the probability that the value will be between 4 and 72 c. What is the mean? d. What is the standard deviation? a. The probability that the value will be between 12 and 17 is (Type an integer or a decimal)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?