(a) What is the probability that there are exactly 2 defective phone batteries in the sample? (b) What is the probability that all phone batteries in the sample are in good condition? (c) “SmartB” needs to pay a large amount of penalty if there are at least 4 defective phone batteries found in the sample. What is the chance that “SmartB” has to pay this penalty?
“SmartB” owns a phone battery assembly line which provide phone battery to a mobile company. It is known that 4% of the batteries produced by “SmartB” are defective. A random sample of 28 phone batteries is selected from the assembly line and will be sent for inspection.
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(a) What is the probability that there are exactly 2 defective phone batteries in the sample?
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(b) What is the probability that all phone batteries in the sample are in good condition?
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(c) “SmartB” needs to pay a large amount of penalty if there are at least 4 defective phone batteries found in the sample. What is the chance that “SmartB” has to pay this penalty?
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(d) The production cost of a phone battery is $100 and the selling price to the mobile company is $500. When the phone battery is found defective within a year, it could be sent back for repairment, which costs “SmartB” $70. Suppose all defective phone battery would be reported by the customer within a year and would be sent back for repairment. Present the
probability distribution function of the profit gained by “SmartB” from a phone battery. (Remark: Profit = revenue – cost) -
(e) Calculate the expectation, variance, and standard deviation of the profit gained by “SmartB” from a phone battery.
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