A private space company is launching a network of about 11,000 satellites to provide internet connectivity globally. Each satellite has fuel to last about seven ​years, upon which it will steer itself into the atmosphere in order to burn up. On average about four satellites per day are expected to do this. Some satellites may not burn up completely and fragments large enough to cause injury may reach the surface of the Earth. The company estimates that about 10 such fragments per satellite on average will reach the surface of the Earth. The probability that the​ company's satellite constellation will cause an injury is 0.39 every seven years. Assume a Poisson distribution for fragments of satellites causing injury. Complete parts​ (a) through​ (d).   ​a) What is the expected number of injuries every seven ​years?   The expected number is   ​(Round to three decimal places as​ needed.) ​b) What is the expected number of injuries per​ year?   The expected number is   ​(Round to three decimal places as​ needed.) ​c) What is the probability of injury in one​ year?   The probability is   ​(Round to three decimal places as​ needed.)

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
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A private space company is launching a network of about

11,000

satellites to provide internet connectivity globally. Each satellite has fuel to last about

seven

​years, upon which it will steer itself into the atmosphere in order to burn up. On average about

four

satellites per day are expected to do this. Some satellites may not burn up completely and fragments large enough to cause injury may reach the surface of the Earth. The company estimates that about 10 such fragments per satellite on average will reach the surface of the Earth. The probability that the​ company's satellite constellation will cause an injury is

0.39

every

seven

years. Assume a Poisson distribution for fragments of satellites causing injury. Complete parts​ (a) through​ (d).

 

​a) What is the expected number of injuries every
seven
​years?
 
The expected number is
 
​(Round to three decimal places as​ needed.)
​b) What is the expected number of injuries per​ year?
 
The expected number is
 
​(Round to three decimal places as​ needed.)
​c) What is the probability of injury in one​ year?
 
The probability is
 
​(Round to three decimal places as​ needed.)
 
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