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we are exploring the following model for fireflies flashing: a firefly flips a biological equivalent of a coin every second. if it comes up heads (probability of 0.1) it lights up for that second; otherwise it does not. for a given firefly, what is the average number of flashes over a minute? what is the spread (standard deviation) of that number? if we have 1000 fireflies in our field of view, what is the expected number of flashes we will see in 10 seconds? if each flash is .1 lumens and we want 40 lumens at least 70% of the time, how many fireflies do we need? we are monitoring 100 fireflies and determine that the number of flashes per minute per firefly is about 7. is this consistent with our model?



Answer :

  • The average flashes per minute is 6.
  • There will be 1000 flashes per 10 seconds.
  • There is 3 fireflies required to produce 40 lumens

Given,

The probability of head ups of a firefly = 0.1 = 10%

  • The average flashes per minute = 10% of 60 seconds = 6 flashes.

The average flashes per minute is 6.

  • If there is 1000 fire flies, number of flashes in 10 seconds.

1 firefly 6 flashes per minute = 0.1 flash per second

Then,

1000 × 0.1 = 100 flashes per second

100 × 10 = 1000 flashes per 10 seconds

There will be 1000 flashes per 10 seconds.

  • How many fireflies are required if each flash produces.1 lumens, and we aim for 40 lumens at least 70% of the time?

Each flash = 0.1 lumen

40 lumens = 4 flash

70/100 = 0.7

0.7 x 4 = 2.8 = 3 fireflies.

There is 3 fireflies required to produce 40 lumens

Learn more about flashes here;

https://brainly.com/question/14333908

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