Suppose that a sample of peanut butter contains 0.3 insect fragments per gram. C

Question

Suppose that a sample of peanut butter contains 0.3 insect fragments per gram. 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. Interpret each result. (a) Exactly five (c) At least five (e) Would it be unusual for a 7-gram sample of this supply of peanut butter to contain seven or more insect fragments? (b) Fewer than five (d) At least one (a) The probability that there are exactly five insect fragments in a 7-gram sample of peanut butter is L0417 (Round to four decimal places as needed.) I insect fragment(s) in about of every 1007-gram samples of peanut butter. There will be (Round to the nearest whole number as needed.) (b) The probability that there are fewer than five insect fragments in a 7-gram sample of peanut butter is (Round to four decimal places as needed.) insect fragment(s) in abo of every 100 7-gram samples of peanut butter. There will be (Round to the nearest whole number as needed.) (c) The probability that there are at least five insect fragments in a 7-gram sample of peanut butter is Round to four decimal places as needed.) There will be Round to the nearest whole number as needed.) inect fragment(s) in aboutof every 100 7-gram samples of peanut butter.

Explanation / Answer

Insect fragments = 7(0.3)=2.1 grams

P(x=k) = e^-2.1 2.1^k / k!

A)
P(x=5) = e^-2.1 (2.1)^5 / 5!
= 0.04165

B)
P( x < 5) = P(x=0)+P(x=1)+P(x=2)+P(x=3)+P(x=4)

P(x=0)=e^-2.1
P(x=1)=e^-2.1 2.1^1 /1!

= 0.1224 + 0.2570 + 0.2699 + 0.1889+0.0991 = 0.9373

C)
P( at least 5) = P( x >= 5) = 1-P( x < 5)
P( x < 5) = 0.9373 (problem B)

1-P( x < 5) = 1-0.9373
= 0.0627

D)
P( at least 1) = P( x >=1)
= 1-P(x=0)
= 1-e^-2.1
= 1-0.1224
= 0.8776

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