SOLUTION: Given 30 questions, if the minimum passing grade is 21, what is the exact probability that a student passes the exam if they are guessing on each question with a 35% chance of gues

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Question 1200895: Given 30 questions, if the minimum passing grade is 21, what is the exact probability that a student passes the exam if they are guessing on each question with a 35% chance of guessing correctly?
Found 2 solutions by ikleyn, Edwin McCravy:
Answer by ikleyn(52946) About Me  (Show Source):
You can put this solution on YOUR website!
.
Given 30 questions, if the minimum passing grade is 21, what is the exact probability
that a student passes the exam if they are guessing on each question with a 35% chance
of guessing correctly?
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The given problem is a Binomial distribution probability problem.


It asks about the probability of getting 21 or more successful trials in the
experiment with 30 trials and the probability of success 0.35 in each individual trial.


The formula for the probability is

    P = P(n=30; k>=21; p=0.35) = sum%28C%5B30%5D%5Ei%2A0.35%5Ei%2A%281-0.35%29%5E%2830-i%29%2Ci=21%2C30%29.


The simplest way to calculate it is to use the 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 = P(n=30, k>=21, p= 0.35) = 0.0001  (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).



Answer by Edwin McCravy(20067) About Me  (Show Source):
You can put this solution on YOUR website!
Your teacher might expect you to use a TI-84 calculator.

It's the probability of getting 30-21=9 or fewer wrong with the probability of
getting a question wrong being 1-0.35=0.65.

press 2nd vars
scroll down to B:binomcdf(
press enter
beside trials: type 30
beside p: type 0.65
beside x value: type 9
press the down arrow to highlight Paste
press enter
you should read binomcdf(30,0.65,9)
press enter
Read 1.001487905E-4

The E-4 means x10-4 (the E is for the exponent of 10)

1.001487905x10-4

which is scientific notation and means to move the decimal point left
4 places.

0.0001001487905

Edwin