Problem #8: Data from the Central Hudson Laboratory determined that the mean num

Question

Problem #8: Data from the Central Hudson Laboratory determined that the mean number of insect fragments in 225-gram chocolate bars was 14.4 (http://www.centralhudsonlab.com/chocolates.shtml). In a 36-gram bar the mean number of insect fragments would then be 2.30. Assume that the number of insect fragments follows a Poisson distribution. (a) If you eat a 36-gram chocolate bar, find the probability that you will have eaten at least 2 insect fragments (b) If you eat a 36-gram chocolate bar every week for 9 weeks, find the probability that you will have eaten no insect fragments in exactly 6 of those weeks Problem #8(a) Problem #8(b) Just Save Submit Problem #8 for Grading Problem #8 Attempt #2 8(a) Attempt #3 8(a) Attempt #1 Your Answer: 8(a) Your Mark: 8(a) 8(b) 8(a) 8(b 8(b) 8(a) 8(b)

Explanation / Answer

Ans:

a)Mean rate =2.3

P(atleast 2)=P(x>=2)

=1-P(x=0)-P(x=1)

=1-e-2.3*(2.30/0!+2.31/1!)

=1-0.3309

=0.6691

b)

P(no insect)=P(x=0)=e-2.3=0.1

Now use binomial distribution with n=9 and p=0.1003

P(y=6)=9C6*0.16*(1-0.1)3=0.0001

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