5) A test consists of 20 multiple choice questions, each with five possible answ
ID: 3364947 • Letter: 5
Question
5) A test consists of 20 multiple choice questions, each with five possible answers, only one of which is correct. Find the mean and the standard deviation of the number of correct answers. A) mean: 10; standard deviation: 1.79 C) mean: 10; standard deviation: 3.16 B) mean: 4; standard deviation: 2 D) mean: 4; standard deviation: 1.79 6) A test consists of 10 true or false questions. To pass the test a student must answer at least eight questions correctly. If the student guesses on each question, what is the probability that the studer will pass the test? A) 0.055 B) 0.08 C) 0.20 D)0.8 Find the area under the standard normal curve between z =-1.5 and z = 25. A) 0.7182 B) 0.9831 C) 0.9270 D) 0.6312Explanation / Answer
5.
BIONOMIAL DISTRIBUTION
pmf of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
where
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial
I.
mean = np
where
n = total number of repetitions experiment is excueted
p = success probability
mean = 20 * 0.2
= 4
II.
variance = npq
where
n = total number of repetitions experiment is excueted
p = success probability
q = failure probability
variance = 20 * 0.2 * 0.8
= 3.2
III.
standard deviation = sqrt( variance ) = sqrt(3.2)
=1.7889
= 1.79
6.
BIONOMIAL DISTRIBUTION
pmf of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
where
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial
I.
mean = np
where
n = total number of repetitions experiment is excueted
p = success probability
mean = 10 * 0.5
= 5
II.
variance = npq
where
n = total number of repetitions experiment is excueted
p = success probability
q = failure probability
variance = 10 * 0.5 * 0.5
= 2.5
III.
standard deviation = sqrt( variance ) = sqrt(2.5)
=1.5811
P( X < 8) = P(X=7) + P(X=6) + P(X=5) + P(X=4) + P(X=3) + P(X=2) + P(X=1) + P(X=0)
= ( 10 7 ) * 0.5^7 * ( 1- 0.5 ) ^3 + ( 10 6 ) * 0.5^6 * ( 1- 0.5 ) ^4 + ( 10 5 ) * 0.5^5 * ( 1- 0.5 ) ^5 + ( 10 4 ) * 0.5^4 * ( 1- 0.5 ) ^6 + ( 10 3 ) * 0.5^3 * ( 1- 0.5 ) ^7 + ( 10 2 ) * 0.5^2 * ( 1- 0.5 ) ^8 + ( 10 1 ) * 0.5^1 * ( 1- 0.5 ) ^9 + ( 10 0 ) * 0.5^0 * ( 1- 0.5 ) ^10
= 0.9453
P( X > = 8 ) = 1 - P( X < 8) = 0.0547 = 0.055
Area between normal curve Z=-1.5 and Z = 2.5
To find P(a < = Z < = b) = F(b) - F(a)
p(-1.5<z<2.5) = P(z<2.5)-p(Z<-1.5)
= 0.99397- 0.066807
= 0.926983 = 0.927
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.