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A pharmaceutical company conducted a study to evaluate the effect of an allergy relief medicine; 250 patients with symptoms that included itchy eyes...

Military radar and missile detection systems are designed to warn a country of enemy attacks. A reliability question deals with the ability of the detection system to identify an attack and issue a warning. Assume that a particular detection system has a 0.90 probability of detecting a missile attack. Answer the following questions using the binomial probability distribution.
a) what is the probability that 1 detection system will detect an attack
b) if 2 detection systems are installed in the same area and operate independently, what is the probability that at least 1 of the systems will detect the attack
c) if 3 systems are installed, what is the probability that at least 1 of the systems will detect an attack?
d) Would you recommend that multiple detection systems be operated? Explain
Note: In addition to the answers, please include the solution(how you arrived at the answers).
A pharmaceutical company conducted a study to evaluate the effect of an allergy relief medicine; 250 patients with symptoms that included itchy eyes and a skin rash received the new drug. The results of the study are as follows: 90 of the patients treated experienced eye relief, 135 had their skin rash clear up, and 45 experienced relief of both itchy eyes and the skin rash. What is the probability that a patient who takes the drug will experience relief of at least one of the two symptoms? Choose one answer. A. 25% B. 72% C. 82% D. 90% Question 2 Marks: 5 The demand for a product of Carolina Industries varies greatly from month to month. Based on the past 2 years of data, the following probability distribution shows the company's monthly demand. Unit Demand Probability 300 0.20 400 0.30 500 0.35 600 0.15 a. If the company places monthly orders equal to the expected value of the monthly demand, what should Carolina's monthly order quantity be for this product? Choose one answer. A. 445 B. any between 300 and 600 C. 500 D. 450 Question 3 Marks: 5 Please refer to Question #2. b. Assume that each unit demanded generates $70 in revenue and that each unit ordered costs $50. How much will the company gain or lose in a month if it places an order based on your answer to the previous question and the actual demand for the item is 300 units?
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Choose one answer. A. $8900, gain B. -$1250, loss C. $6000, gain D. $0, no gain or loss Question 4 Marks: 5 Please refer to Question #2. c. What are the variance and the standart deviation for the number of units demanded? Choose one answer. A. 0.33, 0.57 B. 625, 25 C. 9475, 97.3 D. 9500, 97.5 Question 5 Marks: 5 Military radar and missile detection systems are designed to warn a country of enemy attacks. A reliability question deals with the ability of the detection system to identify an attack and issue the warning. Assume that a particular detection system has a 0.90 probability of detecting a missile attack. Answer the following questions using the binomial probability distribution. a. What is the probability that 1 detection system will detect an attack? Choose one answer. A. 99.9% B. 99% C. 90% D. 81% 6 Marks: 5 Please refer to Question #5. b. If two detection systems are installed in the same area and operate independently, what is the probability that at least 1 of the systems will detect the attack? Choose one answer. A. 90%
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