The lifetime of a mobile phone battery is measured in charge cycles. In a typica

Question

The lifetime of a mobile phone battery is measured in charge cycles. In a typical battery, the maximum number of the charge cycles is normally distributed with mu = 500 and sigma = 30. what is the expectation and variance of the maxim number of the charge cycles in a typical cycles? What is the probability that a battery will survive for more than 550 charge cycles? What is the probability that the life time will be between 470 and 520 charge cycles? What is the number of charge cycles before which the battery will fail with a probability of 70%?

Explanation / Answer

a.expectation of maximum number of charge cycle=meu=500,and variance =sigma^2=900

b.P[x>550]=P[{(x-500)/30}>(550-500)/30}]=P[Z>50/30]

=P[Z>1.667]

=.9515

C.P[470<X<520]=P[(470-500)/30<{(X-500)/30}<(520-500)/30}=P[-1<Z<.666]

=.7454-(.50-.3413)

=.5867

d.

required n=(sigma ^2)/del*E^2

where P[{x-meu}<E}>1-del, here 1-del=70%=.7 that is del=.30

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