Question

The amount of time a certain brand of light bulb lasts is normally distribued with amean of 1200 hours and a standard deviation of 45 hours. Out of 780 freshly installedlight bulbs in a new large building, how many would be expected to last less than1280 hours, to the nearest whole number?

Answer 1

Solution:

Given;

$x=1280,\mu=1200,\sigma=45,n=780$

Then, the z-score;

$\begin{gathered} z=\frac{x-\mu}{\sigma} \\ \\ z=\frac{1280-1200}{45} \\ \\ z=\frac{80}{45} \\ \\ z=1.7778 \end{gathered}$

Thus;

$P(x<1.7778)=0.96228$

Thus, the number of light bulbs that would be expected to last less than 1280 hours is;

$\begin{gathered} 780(0.96228)=750.58 \\ \\ \approx751\text{ light bulbs} \end{gathered}$

ANSWER: 751 light bulbs