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](https://tex.z-dn.net/?f=%5Cmu%3D900%5C%20%3B%5C%20%5Csigma%3D100)
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}](https://tex.z-dn.net/?f=z%3D%5Cdfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D)
For x=820
![z=\dfrac{820-900}{100}=-0.8](https://tex.z-dn.net/?f=z%3D%5Cdfrac%7B820-900%7D%7B100%7D%3D-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](https://tex.z-dn.net/?f=P%28x%3E820%29%3DP%28z%3E-0.8%29%3D1-P%28z%3C-0.8%29)
![1- 0.2118554=0.7881446](https://tex.z-dn.net/?f=1-%200.2118554%3D0.7881446)
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](https://tex.z-dn.net/?f=0.7881446%5Ctimes10000%3D7881.446%5Capprox7881)