Homework SourseThe probability distribution table at the right is of the di
| The probability distribution table at the right is of the discrete random variable x representing the number of cars owned by each family in a specific neighborhood of Wichita, KS. Answer the following: | ||||||||||
| x | P(X=x) | |||||||||
| (a) | Determine the value that is missing in the table. (Hint: what are the requirments for a probability distribution?) | 0 | 0.12 | |||||||
| 1 | ||||||||||
| 2 | 0.24 | |||||||||
| (b) | Find the probability that x is at least 2 , that is find P(x 2). | 3 | 0.11 | |||||||
| 4 | 0.07 | |||||||||
| (c) | Find P(x < 1). Describe what the resulting value represents within the given context. | |||||||||
| (d) | Find the mean (expected value) and standard deviation of this probability distribution. | |||||||||
| (a) | What is meant by the term \"expected value\"? | |||||||||
| (b) | Suppose the expected value of a game of chance is -$2.75. Does this mean that every time one plays this game, she will lose $2.75? Explain your answer briefly. | |||||||||
| List the four requirements needed for an experiment/procedure to be considered a binomial distribution? | ||||||||||
| A company produces a device for the purposes of medical research. As with all production lines of senstive equipment, even when production processes are working correctly, not all devices sent out from the factory are flawless. Suppose the company has found that there is a 15% rate of defect on these devices after shipment. You currently received a shipment of 14 such devices from this company. Use this situation to answer the parts below. | ||||||||||
| (a) | Recognizing that this is a binomial situation, give the meaning S and F in this context. That is, define in words what you will classify as a successful trial and what you will classify as a failure trial when a device is selected and tested for defects. | |||||||||
| S = | ||||||||||
| F = | ||||||||||
| (a) | Next, give the values of n, p, and q. | |||||||||
| (b) | Construct the complete binomial probability distribution for this situation in a table out to the right. | |||||||||
| (c) | Using your table, find the probability that exactly two of the randomly selected devices is defective. | |||||||||
| (d) | Find the probability that at least three of the devices are defective. | |||||||||
| (e) | Find the probability that less than two of the devices are defective. | |||||||||
| (f) | Find the mean and standard deviation of this binomial probability distribution. | |||||||||
| (g) | By writing a sentence, interpret the meaning of the mean value found in (f) as tied to the context of defective devices in a shipment of 14. | |||||||||
| (h) | Is it unusual to have all 14 of the devices in a shipment work correctly? Briefly explain your answer giving supporting numerical evidence. | |||||||||
| The probability distribution table at the right is of the discrete random variable x representing the number of cars owned by each family in a specific neighborhood of Wichita, KS. Answer the following: | ||||||||||
| x | P(X=x) | |||||||||
| (a) | Determine the value that is missing in the table. (Hint: what are the requirments for a probability distribution?) | 0 | 0.12 | |||||||
| 1 | ||||||||||
| 2 | 0.24 | |||||||||
| (b) | Find the probability that x is at least 2 , that is find P(x 2). | 3 | 0.11 | |||||||
| 4 | 0.07 | |||||||||
| (c) | Find P(x < 1). Describe what the resulting value represents within the given context. | |||||||||
| (d) | Find the mean (expected value) and standard deviation of this probability distribution. | |||||||||
| (a) | What is meant by the term \"expected value\"? | |||||||||
| (b) | Suppose the expected value of a game of chance is -$2.75. Does this mean that every time one plays this game, she will lose $2.75? Explain your answer briefly. | |||||||||
| List the four requirements needed for an experiment/procedure to be considered a binomial distribution? | ||||||||||
| A company produces a device for the purposes of medical research. As with all production lines of senstive equipment, even when production processes are working correctly, not all devices sent out from the factory are flawless. Suppose the company has found that there is a 15% rate of defect on these devices after shipment. You currently received a shipment of 14 such devices from this company. Use this situation to answer the parts below. | ||||||||||
| (a) | Recognizing that this is a binomial situation, give the meaning S and F in this context. That is, define in words what you will classify as a successful trial and what you will classify as a failure trial when a device is selected and tested for defects. | |||||||||
| S = | ||||||||||
| F = | ||||||||||
| (a) | Next, give the values of n, p, and q. | |||||||||
| (b) | Construct the complete binomial probability distribution for this situation in a table out to the right. | |||||||||
| (c) | Using your table, find the probability that exactly two of the randomly selected devices is defective. | |||||||||
| (d) | Find the probability that at least three of the devices are defective. | |||||||||
| (e) | Find the probability that less than two of the devices are defective. | |||||||||
| (f) | Find the mean and standard deviation of this binomial probability distribution. | |||||||||
| (g) | By writing a sentence, interpret the meaning of the mean value found in (f) as tied to the context of defective devices in a shipment of 14. | |||||||||
| (h) | Is it unusual to have all 14 of the devices in a shipment work correctly? Briefly explain your answer giving supporting numerical evidence. | |||||||||
Solution
