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November 10th, 2016, 10:25 AM   #1
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Binomial distribution and Poisson help please £20 gift card for amazon

Hi guys really struggling understanding this. Using the formula and finding the probality im finding kina kind. Also how to write it in the calculator correctly.

Please help if you have an understanding

7. A shopkeeper finds that 20% of the cartons containing 6 eggs he receives are damaged. A carton is picked at random, checked and returned to the consignment. The procedure is repeated a further 3 times. What is the probability that out of the 4 cartons inspected

(a) None were undamaged?
(b) At least 3 were undamaged?

N= r= p=??

And possion distribtion one:

8. Calls arrive at a switchboard according to the Poisson distribution. If the average number of calls received in a 5-minute period is 6.7, find the probability that:
(a) There are fewer than 4 calls received in a 5-minute period.
(b) There are more than 7 calls received during a 5-minute period.
(c) There are no calls received in a 1-minute period.



Please show me good examples purely using the formula if you can as im really stupid at this atm and finding it difficult. Anyone that can help me and give me answers and reasoning i will give a £20 gift card on amazon.
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November 10th, 2016, 12:03 PM   #2
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7) is a binomial distribution since the cartons are returned

$p=0.2,~N=4$

a) none were undamaged means all 4 were damaged. The probability of this is

$(0.2)^4 = 0.0016$

b) at least 3 were undamaged so at max 1 was damaged. This is the probability that either 0 or 1 was damaged which is

$(0.8 )^4 + \begin{pmatrix}4 \\ 1\end{pmatrix} (0.2)(0.8 )^3 = 0.8192$
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