5) Suppose that light bulbs are installed sequentially into a socket. If we assume that each light bulb has a mean life of 2 months with a standard deviation of 0.25 months. Let X₁, for i=1,2,3.... denote the independent and identically distributed life time of a bulb installed, then a) What is the probability that each bulb will last for at least 7 months? b) What is the probability that each bulb will last at least 1.5 but at most 2.5 months? c) Find the probability that an average life time of 30 bulbs will be at least 2 months. d) Find the probability that 30 bulbs will last at least 4 years.
5) Suppose that light bulbs are installed sequentially into a socket. If we assume that each light bulb has a mean life of 2 months with a standard deviation of 0.25 months. Let X₁, for i=1,2,3.... denote the independent and identically distributed life time of a bulb installed, then a) What is the probability that each bulb will last for at least 7 months? b) What is the probability that each bulb will last at least 1.5 but at most 2.5 months? c) Find the probability that an average life time of 30 bulbs will be at least 2 months. d) Find the probability that 30 bulbs will last at least 4 years.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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