SOLUTION: We believe that 95% of the population of all Calculus I students consider calculus an exciting subject. Suppose we randomly and independently selected 20 students from the populati

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Question 1178704: We believe that 95% of the population of all Calculus I students consider calculus an exciting subject. Suppose we randomly and independently selected 20 students from the population. If the true percentage is really 95%, find the probability of observing 19 or more of the students who consider calculus to be an exciting subject in our sample of 20.

Answer by ikleyn(53937) About Me  (Show Source):
You can put this solution on YOUR website!
We believe that 95% of the population of all Calculus I students consider calculus an exciting subject.
Suppose we randomly and independently selected 20 students from the population.
If the true percentage is really 95%, find the probability of observing 19 or more of the students
who consider calculus to be an exciting subject in our sample of 20.
~~~~~~~~~~~~~~~~~ 

It is a binomial distribution probability problem.

    - number of trials         n =  20;
    - number of success trials k >= 19;
    - Probability of success on a single trial p = 0.95.



We need calculate  P(n = 20; k >= 19; p=0.95).      


To facilitate calculations, I use an appropriate online (free of charge) calculator at this web-site 

https://stattrek.com/online-calculator/binomial.aspx


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


    P(n=20; k >= 19; p=0.95) = 0.73583952495,   or   0.7358 (rounded).       ANSWER

Solved.

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To see a variety of similar 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).