Solution:
Each question has 4 choices.
So ,
probability of correct answer = 1/4 = 0.25
n = 48
Let X be the number of correct answered questions in this sample.
X follows Binomial(n = 48 , p = 0.25)
p = 0.25
q = 1 - p = 1 - 0.25 = 0.75
n*p = 48 * 0.25 = 12
n*q = 48 * 0.75 = 36
Both np and nq are > 10
So , we use normal approximation to binomial.
According to normal approximation binomial,
X Normal with
Mean = = n*p = 12
Standard deviation = =[n*p*q] = [48*0.25*0.75] = 3
Now ,
P[getting at least 22 correct answers]
= P[X 22]
= P[(X - )/ (22 - )/]
= P[Z (22 - 12)/3]
= P[Z 3.33]
= 1 - P[Z < 3.33]
= 1 - 0.9996 ( use z table)
= 0.0004
The probability is 0.0004
A student answers all 48 questions on a multiple-choice test by guessing. Each question has four...
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