Question #342541

T

he time

that

a laptop battery lasts in everyday use before recharge is needed

is normally

distributed, with a mean of 270 minutes

and

a standard deviation o

f 55 minutes.

a) What is the probability that the battery lasts

more than four hours?

b) What value of

battery

life in minutes is exceeded with 95 % probability?

c) What is the probability

that

the battery lasts exactly

300 minutes?



1
Expert's answer
2022-05-19T11:14:56-0400

Let X=X= the time of a laptop battery: XN(μ,σ2).X\sim N(\mu, \sigma^2 ).

Given μ=270min,σ=55min.\mu=270min, \sigma=55min.

a)


P(X>240)=1P(Z24027055)P(X>240)=1-P(Z\le \dfrac{240-270}{55})

1P(Z0.54545)0.70728\approx1-P(Z\le-0.54545)\approx0.70728

b)


P(X>x)=1P(Zx27055)=0.95P(X>x)=1-P(Z\le \dfrac{x-270}{55})=0.95

x27055=1.6449\dfrac{x-270}{55}=-1.6449

x=27055(1.6449)x=270-55(1.6449)

x=179.53 minx=179.53\ min

c)


P(X=300)=0P(X=300)=0


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