Question

As part of the quality assurance program, a battery company conducts tests on battery life. For a particular AA alkaline battery, the mean life is 19 hours. The useful life of the battery follows a normal distribution with a standard deviation of 1.2 hours.

a. Draw a graph of this distribution

b. About 68% of the batteries failed between

what two values?

c. About 95% of the batteries failed between what two values?

d. Virtually all of the batteries failed between what two values?

e. What percent of the batteries failed between 20.2 and 21.4 hours?

f. What percent of the batteries failed in less than 15.4 hours?

g. What percent of the batteries failed between

16.6 and 22.6 hours?

Answer 1

Given the battery life foillows normal distribution with mean and sd .

b) The PDF curve is plotted below using R.

curve(dnorm(x,19,1.2),xlim=c(10,29), ylab = "Density", main='Normal PDF', col="darkred", lwd = 2)

b)We need to find,

So 68% of batteries failed has life between

b) As in part (b), we ca see

So 95% of batteries failed has life between

d) 99.99% of batteries failed between

So 99.99% of batteries failed has life between

e) The probability,

13.6% percent of batteries failed between 20.2 and 21,4 hours.