8. The lifetimes of bulbs used in a lamp are normally distributed.
A company \(X\) sells bulbs with a mean lifetime of 850 hours and a standard deviation of 50 hours.
- Find the probability of a bulb, from company \(X\), having a lifetime of less than 830 hours.
- In a box of 500 bulbs, from company \(X\), find the expected number having a lifetime of less than 830 hours.
A rival company \(Y\) sells bulbs with a mean lifetime of 860 hours and \(20 \%\) of these bulbs have a lifetime of less than 818 hours.
- Find the standard deviation of the lifetimes of bulbs from company \(Y\).
Both companies sell the bulbs for the same price.
- State which company you would recommend. Give reasons for your answer.