You may need to use the appropriate appendix table or technology to answer this question. Given that z is a standard normal random variable, compute the following probabilities. (Round your answers to four decimal places.) (a) P(0 ≤ z < 0.83) (b) P(-1.53 ≤ Z ≤ 0) (c) P(z > 0.46) (d) P(z ≥ -0.26) (e) P(z <1.50) (f) P(z≤ -0.73) W
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- For the next 6 numbers: Refer to the Management Scientist output of a maximization LP problem. The constraints are defined as follows: Constraint 1: advertising budget ( ) Constraint 2: sales force availability ( ) Constraint 3: production level (=) Constraint 4: retail stores requirement ( ) Optimal Solution Objective Function Value - Variable. Constraint X1 X2 X1 X2 X3 X4 X3 X4 1 2 Variable 1 2 3 3 4 OBJECTIVE COEFFICIENT RANGES 4 Constraint RIGHT HAND SIDE RANGES Value Slack/Surplus Lover Limit 25.000 425.000 150.000 0.000 84.000 50.000 No Lover Linit No Lover Linit Lover Limit 48450.000 0.000 25.000 0.000 0.000 4950.000 1775.000 515.000 0.000 Reduced Costs Dual Prices Current Value 90.000 84.000 70.000 60.000 Current Value 0.000 0.000 0.000 45.000 5000.000 1800.000 600.000 150.000 3.000 0.000 60.000 -17.000 Upper Limit No Upper Linit 90.000 87.000 105.000 Upper Linit 5850.000 No Upper Limit 603.571 200.0004.1 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 monthGiven that Z is a standard normal random variable. What is the value of Z if the area to the right of Z is 0.1401? -1.08 0.1401 1.08 2.16
- 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.)do fastThe average weekly earnings of bus drivers in a city are $950 (that is μ) with a standard deviation of $45 (that is σ). Assume that we select a random sample of 81 bus drivers. What is the probability that the sample mean will be greater than $960? (Keep 4 digits of the result)
- 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?We can use the methods below to control extraneous variables except O Manual control O Design control O Statistical control Randomization O MatchingThe average weekly earnings of bus drivers in a city are $950 (that is μ) with a standard deviation of $45 (that is σ). Assume that we select a random sample of 81 bus drivers. What is the probability that the sample mean will be greater than $960? 0.99 0.66 0.023 1 Sample: n= Mean= SD= Probability[P(X>)]= z= Probability[P(Z)]= Answer: Graph:
- Bad simulations Explain why each of the followingsimulations fails to model the real situation properly:a) Use a random integer from 0 through 9 to representthe number of heads when 9 coins are tossed. b) A basketball player takes a foul shot. Look at a ran-dom digit, using an odd digit to represent a good shot and an even digit to represent a miss.c) Use random numbers from 1 through 13 to represent thedenominations of the cards in a five-card poker hand.Maximize z=4x+5y Subject to: x+y<or=4 x-y>or=-2 x<or=3 x>or=0, y>or=0Find the Inverse Laplace Transform of Y(s) = 12 (s+5)*