Question
Asked Nov 5, 2019
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Assume that random guesses are made for seven multiple choice questions on an SAT​ test, so that there are n=7 trials, each with probability of success​ (correct) given by p=0.25
Find the probability that the number x of correct answers is fewer than
4.
 
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Expert Answer

Step 1

It is given that X ~B(7,0.25).

The PMF of binomial distribution is given by,

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п piq 0,1,2 .., n ; q =1-p P(X=x) ;Otherwise.

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Step 2

The probability that the number X of c...

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Р(х <4)- Р(х -0) + P(х -1)+ P(х -2)+ P(X -3) (025)'0-025)(02s)0-025)- 0.250-025)(023'0-025 7-1 + (1- 7-2 7-3 [())(0.1334)+(7)(0.25) (0.178) (21)(0.0625)(0.2373)+ (35)(0.015625) (0.3164) [0.1334 0.3115+0.3115 +0.1730 0.9294

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