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.
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<pre>
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).       <U>ANSWER</U>
</pre>

Solved.


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To see a variety of similar solved problems, &nbsp;look into the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Solving-problems-on-Binomial-distribution-manually.lesson>Simple and simplest probability problems on Binomial distribution</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Typical-binomial-distribution-probability-problems.lesson>Typical binomial distribution probability problems</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/How-to-calculate-binomial-probabilities-using-Technology.lesson>How to calculate Binomial probabilities with Technology (using MS Excel)</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Solving-problems-on-Binomial-distribution-using-Technology.lesson>Solving problems on Binomial distribution with Technology (using MS Excel)</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Solving-problems-on-Binom-distr-with-Technology-%28using-online-solver%29.lesson>Solving problems on Binomial distribution with Technology (using online solver)</A> 

in this site.


After reading these lessons, &nbsp;you will be able to solve such problems on your own, 

which is your &nbsp;PRIMARY &nbsp;MAJOR &nbsp;GOAL &nbsp;visiting this forum &nbsp;(I believe).