Guess on a 10 question multiple choise test ( 4 choices per question ): If X is

ID: 2931715 • Letter: G

Question

Guess on a 10 question multiple choise test ( 4 choices per question ):

If X is the number of correct guesses, check that X has a binomial distribution. what are;

n= s= p= 1-p=

What is the probability of getting 3 correct answer?

What is the probability of getting at most 3 correct answer?

What is the probability of getting at least 3 correct answer?

What is the probability of passing (6 or more correct)?

What is the probability of getting more than 3 but less than 7 correct answer?

What are the mean and the standard deviation for this distribution?

n=10, p=1/4, q=1-p=3/4

Probability of getting 3 correct Answer => s=>3

p(s=3) = 10C3 * p^3 * q^(7) => 0.250282287597656

Probability of getting at most 3 correct Answer => s=>1 or 2 or 3

P(s<=3) = p(s=0) + p(s=1) + p(s=2) + p(s=3)

= 0.0563135147094727 + 0.187711715698242 + 0.281567573547363 + 0.250282287597656

= 0.775875091552734

= 77.59%

Probability of getting at least 3 correct Answer => s=> 3 or 4 or 5 or 6 or 7 or 8 or 9 or 10

P(s>=3)=1-p(s<3)= 1 - [p(s=0) + p(s=1) + p(s=2)]

= 1 - [0.0563135147094727 + 0.187711715698242 + 0.281567573547363]

= 1 - 0.525592803955078

= 0.474407196044922

= 47.44%

Probability of getting 6 or more correct Answer => s=> 6 or 7 or 8 or 9 or 10

P(s>=6) = p(s=6) + p(s=7) + p(s=8) + p(s=9) + p(s=10)

= 0.0162220001220703 + 0.00308990478515625 + 0.000386238098144531 + 0.0000286102294921875 + 0.00000095

= 0.0197277069091797

= 1.97%

Probability of getting more than 3 and less than 7 correct answers => s=> 4 or 5 or 6

P(3<s<7)= p(s=4) + p(s=5) + p(s=6)

= 0.145998001098633 + 0.0583992004394531 + 0.0162220001220703

= 0.220619201660156

= 22.06%

mean= np = 10*1/4 = 2.5

std.dev=sqrt(npq) = sqrt(10 * 1/4 * 3/4) = sqrt(15/8) = sqrt(1.875) = 1.369306

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