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

Step-by-step 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 :

$z=\dfrac{x-\mu}{\sigma}$

For x=820

$z=\dfrac{820-900}{100}=-0.8$

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

$P(x>820)=P(z>-0.8)=1-P(z$

$1- 0.2118554=0.7881446$

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

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

$0.7881446\times10000=7881.446\approx7881$