Answer to Question #342541 in Statistics and Probability for deepsikha

Question

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?

Answer 1

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

Given $\mu=270min, \sigma=55min.$

a)

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

$$\approx1-P(Z\le-0.54545)\approx0.70728$$

b)

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

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

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

$$x=179.53\ min$$

c)

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