SOLUTION: It has been found that 55% of the tools produced by a certain machine are defective. What is the probability that 50.1% or less will prove defective in a production of 100?

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Question 1194784: It has been found that 55% of the tools produced by a certain machine are defective. What is the probability that 50.1% or less will prove defective in a production of 100?
Answer by ikleyn(52790) About Me  (Show Source):
You can put this solution on YOUR website!
.
It has been found that 55% of the tools produced by a certain machine are defective.
What is the probability that 50.1% or less will prove defective in a production of 100?
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50.1% or less of 100 units is 50 units or less of 100 units.


THEREFORE, the problem's question is the same as to ask


    "What is the probability that 50 units or less will prove to be defective in a production of 100?"


In this formulation, it is the binomial distribution problem with the 
individual probability of success p = 0.55, the number of trials 100 
and the number of success trials 50 or less.


The formula to calculate the probability is


         P = sum%28C%5B100%5D%5Ek%2A0.55%5Ek%2A%281-0.55%29%5E%28100-k%29%2Ck=0%2C50%29 = sum%28C%5B100%5D%5Ek%2A0.55%5Ek%2A0.45%5E%28100-k%29%2C+k=0%2C50%29.


     To facilitate my calculations, I used online calculator at this site  https://stattrek.com/online-calculator/binomial.aspx

     It provides nice instructions  and  a convenient input and output for all relevant options/cases.


          The resulting number is P = 0.18272818469 = 0.1827  (rounded).    ANSWER

Solved.

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If you want to see many similar  (or different)  solved problems,  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 these lessons,  you will be able to solve such problems on your own,
which is your  PRIMARY  MAJOR  GOAL  visiting this forum  (I believe).