Question

Information on extrasolar planets can be discerned from foreign material and dust found in our solar system. Studies show that roughly one in every 100 meteoroids entering the Earth’s atmosphere is actually alien matter from outside our solar system.

(a) Calculate the exact probability that, of the next 300 meteoroids entering the Earth’s atmosphere, at least three meteoroids are alien matter from outside our solar system.

(b) Show which probability distribution gives a closer approximation to the probability in part (a): the Poisson distribution or the normal distribution.

Answer 1

ANSWER::

a)

expected number of meteoroids entering earth atmosphere of next 300 meteoriods = =1*300/100=3

therefore probability that of the next 300 meteoriods entering the earths atmosphere, at least three are alien matter from outside solar system =P(X>=3)=1-P(X<=2)=1- =1-0.4232=0.5768

b)

for above distribution normal distribution gives a closer approximation to the probability in part A

with mean =3 and std deviation =(3)1/2 =1.732

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