Homework Problem. Please Help!

ca91

New Member
#1
I'm having problems mostly with part (b) and (c). Please add every single step and side note you can - including formulas used. I greatly appreciate the help!

A company purchases large shipments of lemons and uses this acceptance smaplong plan: randomly select and test 200 lemons, than accept the whole batch if there is less than two found to be rotten bitter; that is, at most one lemon is bad. If a particular shipment actually has a 3% rate of defects:

a. Using the binomial probability distribution, find the probability that this whole shipment is accepted?

P(Accepted) = P(0) + P(1) = ( 200C0 * (0.03)^0 * (0.97)^200 ) + ( 200C1 * (0.03)^1 * (0.97)^199 ) = 0.0162

b. Show that a normal approximation to this binomial distribution is appropriate.

np = 6 => 5, n(1-p) = 194 => 5

c. Using normal approximation (either with or without continuity correction), find the probability that this whole shipment is accepted?

w/o correction: P(Accepted) = P(X <= 1 | μ = 6, σ^2 = 5.82) = P(Z <= -2.07) = 0.0191
w/ correction: P(Accepted) = P(X <= 1.5 | μ = 6, σ^2 = 5.82) = P(Z <= -1.87) = 0.0311

note: <= stands for 'less than or equal to'
 
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#2
Hi! :welcome:We are glad that you posted here! This looks like a homework question though. Our homework help policy can be found here. We mainly just want to see what you have tried so far and that you have put some effort into the problem. I would also suggest checking out this thread for some guidelines on smart posting behavior that can help you get answers that are better much more quickly.
 

Englund

TS Contributor
#5
b. Show that a normal approximation to this binomial distribution is appropriate.

np = 6 => 5, n(1-p) = 194 => 5
This could really be a quite tricky question, depending on the level of your knowledge. In order to answer this question in a more sophisticated way than I suppose is necessary for your task, follow these steps:

1. Prove that the binomial mgf converges to the normal mgf as n--->inf and p=mu.
2. Show via simulation that the normal approximation works well under the conditions in this example.

I guess your teacher would be glad if you did this :)
 

Dason

Ambassador to the humans
#6
This could really be a quite tricky question, depending on the level of your knowledge. In order to answer this question in a more sophisticated way than I suppose is necessary for your task, follow these steps:

1. Prove that the binomial mgf converges to the normal mgf as n--->inf and p=mu.
2. Show via simulation that the normal approximation works well under the conditions in this example.

I guess your teacher would be glad if you did this :)
My guess is that their instructor is just asking them to verify np >= 5 and n(1-p) >= 5.
 

ca91

New Member
#7
My professor gave us a study guide for the final with the problems solved, but I still did not understand this one quite well. That's all. Thanks for the help! :)