23. A student takes a 10-question, true/false exam a the probability of passing

Question

23. A student takes a 10-question, true/false exam a the probability of passing if the lowest passing grade is 6 correct out of 10. Based on your answer, would it be a good idea not to study and to depend on guessing? nd guesses on each question. Find 24, If 30% probabilities for a sample of 15 people. of the people in a community use the library in one year, find these a. b. c. At most 7 used the library Exactly 7 used the library At least 5 used the library A survey found that 25% of pet owners had their pets bathed professionally rather than doing it themselves. If 18 pet owners are randomly selected, find the probability that exactly five people have their pets bathed professionally. 25,

Explanation / Answer

Q23.
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)
=1.581139
P( X < 6) = P(X=5) + P(X=4) + P(X=3) + P(X=2) + P(X=1) + P(X=0)   
= ( 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
= 0.623047
P( X > = 6 ) = 1 - P( X < 6) = 0.376953

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