MULTIPLE CHOICE. Choose the one alternative that best completes the statement or

Question

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 54) The probability that a house in an urban area will be burglarized is 5%. If 20 houses are randomly 54) selected, what is the mean of the number of houses burglarized? B) 10 A) 0.5 C)1.5 55) According to police sources, a car with a certain protection system will be recovered 94% of the 55) time. If 400 stolen cars are randomly selected, what is the mean and standard deviation of the number of cars recovered after being stolen? A) mean: 122: standard deviation: 22.56 C) mean: 376; standard deviation: 4.75 B) mean: 376; standard deviation: 22.56 D) mean: 122: standard deviation: 4.75 56) A recent survey found that 69% of all adults over 50 wear glasses for driving. In a random sample 56) of 70 adults over 50, what is the mean and standard deviation of those that wear glasses? A) mean: 21.7; standard deviation: 3.87 C) mean: 48.3; standard deviation: 3.87 B) mean: 48.3; standard deviation: 6.95 D) mean: 21.7; standard deviation: 6.95 57) The probability that a tennis set will go to a tiebreaker is 16%. In 420 randomly selected tennis sets, 57) what is the mean and the standard deviation of the number of tiebreakers? A) mean: 67.2; standard deviation: 7.51 C) mean: 63; standard deviation: 8.2 B) mean: 67.2; standard deviation: 8.2 D) mean: 63; standard deviation:7.51 58) Assume that male and female births are equally likely and that the birth of any child does not affect 58) the probability of the gender of any other children. Find the probability of exactly eight boys in ten births. A) 0.176 B) 0.8 C)0.044 D) 0.08 59) A recent survey found that 70% of all adults over 50 wear glasses for driving. In a random sample 59) of 10 adults over 50, what is the probability that at least six wear glasses? A) 0.006 B) 0.200 C) 0.850 D) 0.700 60) The probability that a house in an urban area will be burglarized is 3%. If 25 houses are randomly 60) selected, what is the probability that none of the houses will be burglarized? A) 0.000 B) 0.001 C) 0.030 D) 0.467

Explanation / Answer

54.
probability that a house in an urban area will be burglarized is p = 5%= 0.05
sample size n= 20
mean = n*p = 20*0.05 = 1
55.
probability p = 94% = 0.94
sample size n = 400
mean = n*p = 400*0.94 = 376
standard deviation = sqrt(n*p(1-p)) = sqrt(376*0.06) = 22.56
56.
probability p = 69% =0.69
sample size n = 70
mean = n*p = 70*0.69 = 48.3
standard deviation = sqrt(n*p(1-p)) = sqrt(48.3*0.31) = 3.87
57.
probability p =16% = 0.16
sample size n = 420
mean = n*p = 420*0.16 = 67.2
standard deviation =sqrt(n*p(1-p))= sqrt(67.2*0.84)=7.513
58.
probability that exactly 8 boys in ten births = 8/10 = 0.8
59.
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 * 0.7
= 7
II.
variance = npq
where
n = total number of repetitions experiment is excueted
p = success probability
q = failure probability
variance = 10 * 0.7 * 0.3
= 2.1
III.
standard deviation = sqrt( variance ) = sqrt(2.1)
=1.4491
P( X < 6) = P(X=5) + P(X=4) + P(X=3) + P(X=2) + P(X=1) + P(X=0) +   
= ( 10 5 ) * 0.7^5 * ( 1- 0.7 ) ^5 + ( 10 4 ) * 0.7^4 * ( 1- 0.7 ) ^6 + ( 10 3 ) * 0.7^3 * ( 1- 0.7 ) ^7 + ( 10 2 ) * 0.7^2 * ( 1- 0.7 ) ^8 + ( 10 1 ) * 0.7^1 * ( 1- 0.7 ) ^9 + ( 10 0 ) * 0.7^0 * ( 1- 0.7 ) ^10 +
= 0.1503
P( X > = 6 ) = 1 - P( X < 6) = 0.8497 = 0.85
60.
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 = 25 * 0.03
= 0.75
II.
variance = npq
where
n = total number of repetitions experiment is excueted
p = success probability
q = failure probability
variance = 25 * 0.03 * 0.97
= 0.7275
III.
standard deviation = sqrt( variance ) = sqrt(0.7275)
=0.8529
P( X = 0 ) = ( 25 0 ) * ( 0.03^0) * ( 1 - 0.03 )^25
= 0.467

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