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. [tex]\mu=900\ ;\ \sigma=100[/tex]
Let x be the random variable that represents the length of life of the bulb .
Now , we find the z-score for this :
[tex]z=\dfrac{x-\mu}{\sigma}[/tex]
For x=820
[tex]z=\dfrac{820-900}{100}=-0.8[/tex]
Now, the probability that the length of life of the bulb is more than 820 hours is given by :-
[tex]P(x>820)=P(z>-0.8)=1-P(z<-0.8)[/tex]
[tex]1- 0.2118554=0.7881446[/tex]
Now, the number of bulbs installed in amusement park =10,000
Then , the number that can be expected to last more than 820 hours :-
[tex]0.7881446\times10000=7881.446\approx7881[/tex]
