4. Use Excel to find the following Poisson distribution probabilities. (7.5 poin

Question

4. Use Excel to find the following Poisson distribution probabilities. (7.5 points) The quality control manager of Marilyn's Cookies is inspecting a batch of chocolate-chip cookies that has just been baked. If the production process is in control, the mean number of chip parts per cookie is 6.3. Complete parts a through e. a) What is the probability that in any particular cookie being inspected exactly 7 chip parts will be found? b) What is the probability that in any particular cookie being inspected more than 7 chip parts will be found? c) What is the probability that in any particular d) What is the probability that in any p e What is the probability that in any particular cookie being inspected at most 7 chip parts will be found? articular cookie being inspected at least 7 chip parts will be found? In Excel the probability of exactly X successes uses the formula =POISSON DIST

Explanation / Answer

Let X be number of chips per cookie

X ~ Poisson ( lamda = 6.3)

The Probability distribution of X is

P(X=x) = e -lamda * lamda x / x! x =0,1,2,............

a) P ( Exactly 7 cookie will be found ) =P ( X=7)

if you want find this probabiliies by using EXcel use Function POISSON ( 6.3 , 7 , False)

Using Excel P(X=7) = 0.1435

P ( Exactly 7 cookie will be found ) = 0.1435

b) P(More than 7 chip parts will be found) = P(X>7) = 1- P(X<=7)

P(X<=7) =F(7) = Cumulative probability at X=7

By using Excel P(X<=7) = 0.7017 ( Using Function POISSON ( 7,6.3,true)

P(X>7) = 1- 0.7017 = 0.2983

P(More than 7 chip parts will be found) = 0.2983

c) P( Less than 7 chip parts will be found) =P(X <7) =P(X<=6)

Which is cumulative probability at X =6

By using excel

P(X<=6) = 0.5582   ( Using Function POISSON ( 6, 6.3, true)

P( Less than 7 chip parts will be found) = 0.5582

d) P( at least 7 chip parts will be found) = P(X>=7) = 1- P(X<=6)

= 1- 0.5582

= 0.4418

P( at least 7 chip parts will be found) = 0.4418

e) P( At most 7 chip parts will be found ) = P(X<=7)

P(X<=7) =0.7017

P( At most 7 chip parts will be found ) = 0.7017

Table

Probabilities Function Value of Probability P(X=7) POISSON(7,6.3,False) 0.1435 P(X<=7) POISSON(7,6.3,True) 0.7017 P(X<=6) POISSON(6,6.3,True) 0.5582

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