SOLUTION: The probability that a life bulb will have a life time of more than 680 hours is 0.9788. The probability that a bulb will have a life time of more than 700 hours is 0.0051. Find t

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Question 1182589: The probability that a life bulb will have a life time of more than 680 hours is 0.9788. The probability that a bulb will have a life time of more than 700 hours is 0.0051. Find the probability that a bulb will last for more than 648 hours.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
P%28X+%3E+680%29+=+P%28Z+=+%28X-mu%29%2Fsigma+%3E+%28680-mu%29%2Fsigma%29+=+0.9788 ===> %28680-mu%29%2Fsigma+=+-2.030, or 680+-+mu+=+-2.030%2Asigma.

Similarly,
P%28X+%3E+700%29+=+P%28Z+=+%28X-mu%29%2Fsigma+%3E+%28700-mu%29%2Fsigma%29+=+0.0051 ===> %28700-mu%29%2Fsigma+=+2.569, or 700+-+mu+=+2.569%2Asigma.

Now solve for mu and sigma from the two equations above. The values would be

sigma+=+4.35 to 2 d.p., and mu+=+688.83 to 2 d.p.

===> P%28X+%3E+648%29+=+P%28Z+%3E++%28648-688.83%29%2F4.35+=+-9.39%29+=++1.

***We assume that lifetimes are normally distributed, and the probabilities were taken from https://stattrek.com/online-calculator/normal.aspx.