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Binomial, Poisson and Normal Probability distribution help!!
Hey everyone, I've just started a new section on probability (argh) in my math course, and unlike most other maths, I cannot cope!! Anyway, I was wondering if anyone could tell me if I did the following question correctly! Any helps greatly appreciated guys!! Thanks.
Q1. A chocolate factory makes gigantic “death by chocolate” chocolate bars and finds that,
in the long run, approximately 10% of the individual squares contain so much chocolate
to present a health hazard to people consuming them. Every chocolate bar contains 100
squares.
(a) Using the Binomial, Poisson and Normal distributions, write down formulas for
the probability that a single chocolate bar has at least 3 but no more than 7 deadly
squares.
(b) Use either your calculator or the Scientific Notebook functions BinomialDist, PoissonDist
and NormalDist to estimate each of these probabilities.
Does anyone know if this question would be referring to a Cumulative Probability Distribution Function, or a Probability Mass function? (Important!!)
Q2.John teaches two courses in second semester, MTH1122 and MTH1030. Among
John’s students 20 percent are MTH1122 students. As a consequence of John’s
teaching technique 10 percent of the MTH1030 students and 5 percent of the MTH1122
students develop an addiction to mathematics (wishful thinking, or course, but...).
a) What is the probability that one of John’s students who has been randomly chosen
is a matheholic? (5 marks)
b) One of John’s students presents at the doctors with acute symptoms of maths addiction.
What is the probability that this student is an MTH1030 matheholic?
This question assumes:A student who takes one course, does not take the other course. There were no matheholics among the students before Burkard started teaching the course.
MY ANSWERS:
Q1. (a) Binomial: Using, n=100, p=0.10 and I calculated the formula as:
Pr(3[greater than or equal to]P[less than or equal to]7)=((100!)/(3!*97!)*((0.10)^3)*((0.90)^97) + ........ + ((100!)/(7!*93!)*((0.10)^7)*((0.90)^93)
Poisson: I calculated the mean, as E(p)=np=100*0.10=10
therefore, Pr(3[greater than or equal to]P[less than or equal to]7)=([exp]^(10)*((10^3)/3!)) + ........+([exp]^(10)*((10^7)/7!))
Normal: Using the mean (E(P)) to get the standard deviation of P (stdev(p)=(Var(P))^(1/2)
Pr(3[greater than or equal to]P[less than or equal to]7)= [Integral: upper limit=7, lower limit=3] of ((1)/3((2pi)^(1/2))*[exp]^(0.5(((x10)/3)^2)
(b) For (b), I used excel, however I don't know whether this question is a 'Cumulative Probability Distribution Function' or a 'Probability Mass Function'. Anyone know?? Because, using Excel, if I use a CDF(for Binomial), I get the above probability as 0.412331, and if I use a PMF, i get the above probability as 0.204706.
Q2. For this question, it looks and sounds really easy, but I don't trust my mischievous lecturer (as this question is worth 10 marks out of a 50 mark assignment).
Firstly I set up a tree diagram:(see attached picture), where M=probability a student is a 'matheholic'
(a) For question a, I said: Pr(M)= Pr(MTH1122 student AND a matheholic) + Pr(MTH1030 student AND a matheholic)=(0.20*0.05) + (0.80*0.10)=0.09
(b) I set it up as a conditional probability question: Pr(MTH1030 MatheholicM)= Pr(MTH1030 Matheholic AND M)/ Pr(M)=0.08/0.09=0.889
Again, ANY Help at all is greaatly appreciated, and thanks for your time!!
Hey everyone, I've just started a new section on probability (argh) in my math course, and unlike most other maths, I cannot cope!! Anyway, I was wondering if anyone could tell me if I did the following question correctly! Any helps greatly appreciated guys!! Thanks.
Q1. A chocolate factory makes gigantic “death by chocolate” chocolate bars and finds that,
in the long run, approximately 10% of the individual squares contain so much chocolate
to present a health hazard to people consuming them. Every chocolate bar contains 100
squares.
(a) Using the Binomial, Poisson and Normal distributions, write down formulas for
the probability that a single chocolate bar has at least 3 but no more than 7 deadly
squares.
(b) Use either your calculator or the Scientific Notebook functions BinomialDist, PoissonDist
and NormalDist to estimate each of these probabilities.
Does anyone know if this question would be referring to a Cumulative Probability Distribution Function, or a Probability Mass function? (Important!!)
Q2.John teaches two courses in second semester, MTH1122 and MTH1030. Among
John’s students 20 percent are MTH1122 students. As a consequence of John’s
teaching technique 10 percent of the MTH1030 students and 5 percent of the MTH1122
students develop an addiction to mathematics (wishful thinking, or course, but...).
a) What is the probability that one of John’s students who has been randomly chosen
is a matheholic? (5 marks)
b) One of John’s students presents at the doctors with acute symptoms of maths addiction.
What is the probability that this student is an MTH1030 matheholic?
This question assumes:A student who takes one course, does not take the other course. There were no matheholics among the students before Burkard started teaching the course.
MY ANSWERS:
Q1. (a) Binomial: Using, n=100, p=0.10 and I calculated the formula as:
Pr(3[greater than or equal to]P[less than or equal to]7)=((100!)/(3!*97!)*((0.10)^3)*((0.90)^97) + ........ + ((100!)/(7!*93!)*((0.10)^7)*((0.90)^93)
Poisson: I calculated the mean, as E(p)=np=100*0.10=10
therefore, Pr(3[greater than or equal to]P[less than or equal to]7)=([exp]^(10)*((10^3)/3!)) + ........+([exp]^(10)*((10^7)/7!))
Normal: Using the mean (E(P)) to get the standard deviation of P (stdev(p)=(Var(P))^(1/2)
Pr(3[greater than or equal to]P[less than or equal to]7)= [Integral: upper limit=7, lower limit=3] of ((1)/3((2pi)^(1/2))*[exp]^(0.5(((x10)/3)^2)
(b) For (b), I used excel, however I don't know whether this question is a 'Cumulative Probability Distribution Function' or a 'Probability Mass Function'. Anyone know?? Because, using Excel, if I use a CDF(for Binomial), I get the above probability as 0.412331, and if I use a PMF, i get the above probability as 0.204706.
Q2. For this question, it looks and sounds really easy, but I don't trust my mischievous lecturer (as this question is worth 10 marks out of a 50 mark assignment).
Firstly I set up a tree diagram:(see attached picture), where M=probability a student is a 'matheholic'
(a) For question a, I said: Pr(M)= Pr(MTH1122 student AND a matheholic) + Pr(MTH1030 student AND a matheholic)=(0.20*0.05) + (0.80*0.10)=0.09
(b) I set it up as a conditional probability question: Pr(MTH1030 MatheholicM)= Pr(MTH1030 Matheholic AND M)/ Pr(M)=0.08/0.09=0.889
Again, ANY Help at all is greaatly appreciated, and thanks for your time!!
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