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Can you help me to understand the answer to this question?

Question: Among companies doing highway/bridge construction. 81% test employees for substance abuse. A study involves the random selection of 8 companies.

a) Find the probability that at least half (4 or more) of the companies test for substance abuse.

answer:

X P(x)

0 .000002

1 .000058

2 .000864

3 .007369

4 .039269

5 .133929

6 .285480

7 .347787

8 .185302

= .99171

My teacher gave us the answer key and I don't understand how he got the values in the table. Can anyone explain that to me?

1 Answer

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  • 9 years ago
    Favorite Answer

    The values in the table are from the Binomial Distribution.

    X ~ Bin(8,0.81) because there are 8 trials (n=8) with the probability of 81% of success in each (p=.81).

    The probabilities in the table are from P(x) = (nCx)*p^x*(1-p)^(n-x)

    Where nCx is n!/x!(n-x)!

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