A different student studied a little and can make an educated guess on all 20questions, improving his odds of guessing it correctly up to 0.50. What are the oddsthat this second student gets a failing grade? That is: he gets less than 12 questionscorrect out of the 20 questions?0.12010.25170.87990.83980.74830.13160.16020.58520.8684

Answered: A different student studied a little…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Expert Solution

Step 1: Obtained probability using binomial distribution.

Let X be the number of questions correctly answered out of n=20 questions.

p=Probability of correct guess = 0.5.

Then X has binomial distribution Bin (20, 0.5).Therefore,

P(X<12) = P(X $less or equal than$ 11) = $sum from 0 to 11 of open parentheses table row 20 row x end table close parentheses left parenthesis 0.5 right parenthesis to the power of x space left parenthesis 1 minus 0.5 right parenthesis to the power of 20 minus x end exponent space equals space stack sum with 0 below and 11 on top open parentheses table row cell 20 end cell row cell x end cell end table close parentheses left parenthesis 0.5 right parenthesis to the power of 20$ =0.7483