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March 9th, 2017, 03:54 AM   #1
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Probability Distributions

A wheat miller will only accept a consignment of wheat if the wheat has dried out completely. From past experience, the miller knows that approximately 15% of all wheat bags delivered is too wet to be processed immediately. If a random sample of 6 bags are drawn from each consignment he receives, find the probability that:
2.1.1. Exactly 3 bags being too wet
2.1.2. Less than 4 bags being too wet
2.1.3. At least 5 bags being too wet
2.1.4. Exactly 2 bags being dry enough

Any help is greatly appreciated! i don't know how use these questions in the formula..
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March 9th, 2017, 04:12 AM   #2
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Originally Posted by Kyle0607 View Post
A wheat miller will only accept a consignment of wheat if the wheat has dried out completely. From past experience, the miller knows that approximately 15% of all wheat bags delivered is too wet to be processed immediately. If a random sample of 6 bags are drawn from each consignment he receives, find the probability that:
2.1.1. Exactly 3 bags being too wet
2.1.2. Less than 4 bags being too wet
2.1.3. At least 5 bags being too wet
2.1.4. Exactly 2 bags being dry enough

Any help is greatly appreciated! i don't know how use these questions in the formula..
Each time you test a bag, the only possibilities are wet or dry. As each trial only ever has two possibilities, that means the distribution is binomial.
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March 9th, 2017, 04:23 AM   #3
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Each time you test a bag, the only possibilities are wet or dry. As each trial only ever has two possibilities, that means the distribution is binomial.
So would i be correct in saying
2.2.1) 0.27648
2.2.2) 0.04096
2.2.3) 0.995904
2.2.4) 0.059535
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March 9th, 2017, 12:36 PM   #4
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Originally Posted by Kyle0607 View Post
So would i be correct in saying
2.2.1) 0.27648
2.2.2) 0.04096
2.2.3) 0.995904
2.2.4) 0.059535
these numbers aren't what I get at all

$p(k) = \binom{n}{k}p^k (1-p)^{n-k}$

$p(k)=\binom{6}{k}(0.15)^k(0.85)^{6-k}$

1) $p(3) = \binom{6}{3}(0.15)^3(0.85)^3 \approx 0.0414534$

similar for the others. Try again or show how you came about the above results.
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