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

Given;

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

Then, the z-score;

`\begin{gathered} z=(x-\mu)/(\sigma) \\ \\ z=(1280-1200)/(45) \\ \\ z=(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