5. The lifetimes of batteries sold by company \(X\) are normally distributed, with mean 150 hours and standard deviation 25 hours.
A box contains 12 batteries from company \(X\).
- Find the expected number of these batteries that have a lifetime of more than 160 hours.
The lifetimes of batteries sold by company \(Y\) are normally distributed, with mean 160 hours and \(80 \%\) of these batteries have a lifetime of less than 180 hours.
- Find the standard deviation of the lifetimes of batteries from company \(Y\).
Both companies sell their batteries for the same price.
- State which company you would recommend. Give reasons for your answer.