Practise converting normal areas and percentiles into raw-value boundaries, then rearrange the z-score relationship to recover an unknown mean or operating setting.
A company that manufactures smartphones developed a new battery that has a longer life span than that of a traditional battery. From the date of purchase of a smartphone, the distribution of the life span of the new battery is approximately normal with mean 30 months and standard deviation 8 months. For the price of $50, the company offers a two-year warranty on the new battery for customers who purchase a smartphone. The warranty guarantees that the smartphone will be replaced at no cost to the customer if the battery no longer works within 24 months from the date of purchase.
In how many months from the date of purchase is it expected that 25 percent of the batteries will no longer work? Justify your answer.
Part (a):
The 25 th percentile of the standard normal distribution is -0.6745. Consequently the 25 th percentile of a normal distribution with mean 30 months and standard deviation 8 months is 30+8(-0.6745)=24.6 months.