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vovangra [49]
3 years ago
14

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 th

e 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.
Mathematics
1 answer:
Allisa [31]3 years ago
6 0

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

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