SOLUTION: The chance that a U.S. police chief believes the death penalty "significantly reduces the number of homicides" is one in four. If a random sample of eight police chiefs is selected

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Question 1171779: The chance that a U.S. police chief believes the death penalty "significantly reduces the number of homicides" is one in four. If a random sample of eight police chiefs is selected, find the probability that at most three believe that the death penalty significantly reduces the number of homicides.
Answer by ikleyn(52775) About Me  (Show Source):
You can put this solution on YOUR website!
.

            It is a binomial distribution type problem.

            I will use the Excel standard function BINOM.DIST to facilitate calculations.
            It has the analogue --- the standard function binompdf in pocket calculators TI-83 and TI-84. 


Probability that at most three of 8 do believe is 


    P = P(0) + P(1) + P(2) + P(3) = sum%28C%288%2Ck%29%2A0.25%5Ek%2A%281-0.25%29%5E%288-k%29%2Ck=0%2C3%29 = BINOM.DIST(3, 8, 0.25, TRUE) = 0.8862 = 88.62%.      ANSWER


The Excel standard function BINOM.DIST allows calculating this sum in one click.

Solved.

On Excel function BINOM.DIST, see its description everywhere, for example
https://support.office.com/en-us/article/binom-dist-function-c5ae37b6-f39c-4be2-94c2-509a1480770c


On binompdf function for pocket calculators TI-83 and TI-84 see the link
http://users.rowan.edu/~schultzl/ti/binomial.pdf


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    - How to calculate Binomial probabilities using Technology
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