A normally distributed random variable has a mean of 240 and a standard deviation of 172 what is the probability that x is greater than 269? (Enter your answer to 3 decimal places)
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- Dilberts Department Store is trying to determine how many Hanson T-shirts to order. Currently the shirts are sold for 21, but at later dates the shirts will be offered at a 10% discount, then a 20% discount, then a 40% discount, then a 50% discount, and finally a 60% discount. Demand at the full price of 21 is believed to be normally distributed with mean 1800 and standard deviation 360. Demand at various discounts is assumed to be a multiple of full-price demand. These multiples, for discounts of 10%, 20%, 40%, 50%, and 60% are, respectively, 0.4, 0.7, 1.1, 2, and 50. For example, if full-price demand is 2500, then at a 10% discount customers would be willing to buy 1000 T-shirts. The unit cost of purchasing T-shirts depends on the number of T-shirts ordered, as shown in the file P10_36.xlsx. Use simulation to determine how many T-shirts the company should order. Model the problem so that the company first orders some quantity of T-shirts, then discounts deeper and deeper, as necessary, to sell all of the shirts.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 month
- The random variable X has a uniform distribution with values between the interval 37 to 41. What is the mean and standard deviation of X?5. Use @RISK to draw a triangular distribution withparameters 300, 500, and 900. Then answer the following questions.a. What are the mean and standard deviation of thisdistribution?b. What are the 5th and 95th percentiles of this distribution?c. What is the probability that a random number fromthis distribution is less than 450?d. What is the probability that a random number fromthis distribution is greater than 650?e. What is the probability that a random number fromthis distribution is between 500 and 700?A normally distributed population has a mean of 578 and a standard deviation of 7.50. Find the probability that the mean of a sample of size 100 drawn from this population is between 570 and 580. 4621 0 9962 None of the other 3 answers
- 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?A normal population has σ = 4. A random samplehas: n = 50 and X-bar = 22. Find the 90% PI for asingle new value from the population.If two variables are highly correlated, does this imply that changes in one cause changes in the other? If not, give at least one example from the real world that illustrates what else could cause a high correlation.
- Use @RISK to draw a triangular distribution with parameters 300, 500, and 900. Then answer the following questions.a. What are the mean and standard deviation of this distribution?b. What are the 5th and 95th percentiles of this distribution?c. What is the probability that a random number from this distribution is less than 450?d. What is the probability that a random number from this distribution is greater than 650?e. What is the probability that a random number from this distribution is between 500 and 700?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)Bill Hardgrave, production foreman for the Virginia Fruit Company, estimates that the average sales of oranges is 4,700 and the standard deviation is 500 oranges. Sales follow a normal distribution.a) What is the probability that sales will be greater than 5,500 oranges?b) What is the probability that sales will be greater than 4,500 oranges?c) What is the probability that sales will be less than 4,900 oranges?d) What is the probability that sales will be less than 4,300 oranges?