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I will solve part 1b, ONLY.
It is the binomial distribution problem.
- number of trials n = 360;
- number of success trials 50 <= k <= 70;
- Probability of success on a single trial p = 1/6.
We need calculate P(n=360; 50 <= k <= 70; p=1/6).
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.
So, P(n=360; 50 <= k <= 70; p=0.166667) = here I should re-write it using the CUMULATIVE probabilities =
= P(n=360; k <= 70; p=0.166667) - P(n=360; k <= 49; p=0.166667) =
= 0.92893071364 - 0.06601515035 = 0.862915563 = 0.8629 = 86.29% (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).