SOLUTION: 36% of adults say cashews are their favorite kind of nut. You randomly select 12 adults and ask each to name his or her favorite nut. Find the probability that the number who say

Algebra ->  Probability-and-statistics -> SOLUTION: 36% of adults say cashews are their favorite kind of nut. You randomly select 12 adults and ask each to name his or her favorite nut. Find the probability that the number who say       Log On


   

Question 1202021: 36% of adults say cashews are their favorite kind of nut. You randomly select 12 adults and ask each to name his or her favorite nut.
Find the probability that the number who say cashews are their favorite nut is between 4 to 6, inclusive? Note: Inclusive
Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
.


        It is a typical binomial distribution probability problem. 


The number of trials is 12.

The probability of a single success trial is 36% = 0.36.

The number of success trials is between 4 to 6 inclusive, i.e. 4, 5, 6.



Use the standard formula for the probability


    P = sum%28C%5B12%5D%5Ek%2A0.36%5Ek%2A%281-0.36%29%5E%2812-k%29%2Ck=4%2C6%29 = 

      = C%5B12%5D%5E4%2A0.36%5E4%2A0.64%5E8 + C%5B12%5D%5E5%2A0.36%5E5%2A0.64%5E7 + C%5B12%5D%5E6%2A0.36%5E6%2A0.64%5E6 = 

      = 495%2A0.36%5E4%2A0.64%5E8 + 792%2A0.36%5E5%2A0.64%5E7 + 924%2A0.36%5E6%2A0.64%5E6 = 0.5829  (rounded).    ANSWER

Solved.

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If you want to see many other similar  (and different)  solved problems of this type,  look into the lessons

    - Simple and simplest probability problems on Binomial distribution
    - Typical binomial distribution probability problems
    - How to calculate Binomial probabilities with Technology (using MS Excel)
    - Solving problems on Binomial distribution with Technology (using MS Excel)
    - Solving problems on Binomial distribution with Technology (using online solver)
in this site.

After reading from these lessons,  you will be able to solve such problems on your own,  which is your
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