In a certain congressional district, it is known that 30% of the registered vote
ID: 3358994 • Letter: I
Question
In a certain congressional district, it is known that 30% of the registered voters classify themselves as conservatives. If ten district, what is the probability that two of them will be conservatives? (Round your answer to four decimal places.) registered voters are selected at random from this Need Help? wae Taktetor points As part of its quality-contrel program, the video-game oVDs produced by Starr Communications are subjected to a final Inspection before shipment. A sample of eight DVDs Is selected at random from each lot of DVDs produced, and the lot is rejected if the sample contains one or more defective ovo. |f1.5% of the DVDs produced by Starr is defective, find the probability that a shipment will be accepted. (Round your answer to four decimal places.) Need Help? IMosteTak titerExplanation / Answer
Q3.
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 * 0.3
= 3
II.
variance = npq
where
n = total number of repetitions experiment is excueted
p = success probability
q = failure probability
variance = 10 * 0.3 * 0.7
= 2.1
III.
standard deviation = sqrt( variance ) = sqrt(2.1)
=1.449138
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 * 0.3
= 3
II.
variance = npq
where
n = total number of repetitions experiment is excueted
p = success probability
q = failure probability
variance = 10 * 0.3 * 0.7
= 2.1
III.
standard deviation = sqrt( variance ) = sqrt(2.1)
=1.449138
P( X = 2 ) = ( 10 2 ) * ( 0.3^2) * ( 1 - 0.3 )^8
= 0.233474
Q4.
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 = 8 * 0.015
= 0.12
II.
variance = npq
where
n = total number of repetitions experiment is excueted
p = success probability
q = failure probability
variance = 8 * 0.015 * 0.985
= 0.1182
III.
standard deviation = sqrt( variance ) = sqrt(0.1182)
=0.343802
P( X < 1) = P(X=0)
= ( 8 0 ) * 0.015^0 * ( 1- 0.015 ) ^8
= 0.886115