In ENJOY hotel, there are a total of 200 rooms. 160 rooms are ordinary-sized, and the rest are suites. For the ordinary-sized rooms, 80 of them have garden views while the remaining ones have sea views. All suites have sea views. An inspector will randomly inspect a room. (a) What is the probability that a randomly selected room is a suite? (b) Given that a room has sea view is selected, what is the probability that it is a suite? (c) What is the probability that the room is an ordinary-sized room, if this selected room has garden view? A senior inspector will inspect 10 rooms this week. (d) To have a fair representation, how many sea-view rooms and how many garden-view rooms should be inspected? “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.
In ENJOY hotel, there are a total of 200 rooms. 160 rooms are ordinary-sized, and the rest are suites. For the ordinary-sized rooms, 80 of them have garden views while the remaining ones have sea views. All suites have sea views.
An inspector will randomly inspect a room.
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(a) What is the probability that a randomly selected room is a suite?
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(b) Given that a room has sea view is selected, what is the probability that it is a suite?
-
(c) What is the probability that the room is an ordinary-sized room, if this selected room has garden view?
A senior inspector will inspect 10 rooms this week.
(d) To have a fair representation, how many sea-view rooms and how many garden-view rooms should be
inspected?
“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?
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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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