The lifetime of a aaa battery is normally distributed with m

The lifetime of a aaa battery is normally distributed with mean =28.5 and standard deviation = 5.3 hours. For a battery selected random, what is the probability that the lifetime will be between 25 and 34 hours?

Solution

x = observed value
µ = mean (28.5 hours)
= standard deviation (5.3 hours)

between 25 hours and 34 hours

P(25<x<34) = (1 - 25.5% - 14.9%) = 59.6%

as 1st we calculate

P(x<25) = (x - µ) /
P(x<25) = (25 - 28.5) / 5.3
P(x<25) = (-3.5) / 5.3 = -0.6604

The area under the standard normal curve
corresponding to a z-value of -0.6604 is .2454 or 24.5%.
0.5 - 0.245 = .255 or 25.5%.

then we will calculate

P(x>34) = (x - µ) /
P(x<25) = (34 - 28.5) / 5.3
P(x<25) = (5.5) / 5.3 = 1.0377

The area under the standard normal curve
corresponding to a z-value of 1.0377 is .3508 or 35.1%.
0.5 - 0.351 = 0.149 or 14.9%
for finding the required probability we will subtract both from 1

as P(25<x<34) = (1 - 25.5% - 14.9%) = 59.6%