"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. (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?" (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.
"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. (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?" (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.
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 11ECP: A manufacturer has determined that a machine averages one faulty unit for every 500 it produces....
Related questions
Question
100%
c, d and e
Transcribed Image Text:"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.
(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?
(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.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 4 images
Recommended textbooks for you