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Math Question...need help Statistics?
This is a Poisson Distribution Problem:
Suppose that a 7-gram sample of peanut butter contains 0.4 insect fragments. Compute the probability that the number of insect fragments in a 7-gram sample of peanut butter is each of the following values or range of values:
A) Exactly four
B) Fewer than four
C) At least four
D) At least one
2 Answers
- Anonymous1 decade agoFavorite Answer
nCr(p)^r(q)^n-r
- cidyahLv 71 decade ago
Insect fragments = 7(0.4)=2.8 grams
P(x=k) = e^-2.8 2.8^k / k!
A)
P(x=4) = e^-2.8 (2.8)^4 / 4!
= 0.15574
B)
P( x < 4) = P(x=0)+P(x=1)+P(x=2)+P(x=3)
P(x=0)=e^-2.8
P(x=1)=e^-2.8 2.8^1 /1!
etc.
= 0.06081 + 0.170268 + 0.238375 + 0.222483 = 0.691936
C)
P( at least 4) = P( x >= 4) = 1-P( x < 4)
P( x < 4) = 0.691936 (problem B)
1-P( x < 4) = 1-0.691936
= 0.308064
D)
P( at least 1) = P( x >=1)
= 1-P(x=0)
= 1-e^-2.8
= 1-0.06081
= 0.93919
