The safety lock of an industrial appliance must be changed frequently, in order to avoid breakage due to the end of its useful life. Previous studies admit that this service life can be represented by a continuous random variable, assuming values between 0 and 1 year. The probability density function of the lifetime (in years) of the lock is as follows: Based on this information, answer each alternative: a) The probability that the useful life does not reach 5.5 months is: b) The probability that it lasts longer than 8.0 months given that it has been running for 7.0 months is: c)The probability that it will last at least 3.5 but not more than 8.0 months is: d)One unit has been known to last less than 7.5 months. What is the probability that it lasted at least 3.5 months? e)Knowing that the lock has been working for 4.5 months, the probability that the service life is less than 5.5 months is:
The safety lock of an industrial appliance must be changed frequently, in order to avoid breakage due to the end of its useful life. Previous studies admit that this service life can be represented by a continuous random variable, assuming values between 0 and 1 year.
The probability density
Based on this information, answer each alternative:
a) The probability that the useful life does not reach 5.5 months is:
b) The probability that it lasts longer than 8.0 months given that it has been running for 7.0 months is:
c)The probability that it will last at least 3.5 but not more than 8.0 months is:
d)One unit has been known to last less than 7.5 months. What is the probability that it lasted at least 3.5 months?
e)Knowing that the lock has been working for 4.5 months, the probability that the service life is less than 5.5 months is:
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