Question

A certain type of light bulb has an average life of 900 ​hours, with a standard deviation of 100 hours. The length of life of the bulb can be closely approximated by a normal curve. An amusement park buys and installs 10 comma 000 such bulbs. Find the total number that can be expected to last more than 820 hours.

Answer 1

Answer: 7881

Explanation:

Given : A certain type of light bulb has an average life of 900 ​hours, with a standard deviation of 100 hours.

i.e.
`\mu=900\ ;\ \sigma=100`

Let x be the random variable that represents the length of life of the bulb .

Now , we find the z-score for this :

`z=(x-\mu)/(\sigma)`

For x=820

`z=(820-900)/(100)=-0.8`

Now, the probability that the length of life of the bulb is more than 820 hours is given by :-

`P(x>820)=P(z>-0.8)=1-P(z<-0.8)`

`1- 0.2118554=0.7881446`

Now, the number of bulbs installed in amusement park =10,000

Then , the number that can be expected to last more than 820 hours :-

`0.7881446*10000=7881.446\approx7881`