The lifetime, \(L\) , of light bulbs made by a company follows a normal distribution.
\(L\) is measured in hours. The normal distribution curve of \(L\) is shown below.

Write down the mean lifetime of the light bulbs.

The standard deviation of the lifetime of the light bulbs is \(850\) hours.

Find the probability that \(5000 \leqslant L \leqslant 6000\) , for a randomly chosen light bulb.

The company states that \(90\% \) of the light bulbs have a lifetime of at least \(k\) hours.

Find the value of \(k\) . Give your answer correct to the nearest hundred.

\(5800\)       (A1)   (C1)

\(0.420\,\,\,(0.419703...)\)        (A2)(ft) (C2)

\(4710.68...\)       (A2)(ft)

\( = 4700\)           (A1)(ft)      (C3)

Question 8: Normal distribution
Part (a) was correctly answered by the majority.

Part (b) was generally well attempted by those who had studied this part of the course. However, it was clear that many centres simply do not teach this part of the course.

In part (c), the two common faults were calculation of the bottom “tail” and incorrect rounding.