2. A certain sports car comes equipped with either an automatic or a manual tran

Question

2. A certain sports car comes equipped with either an automatic or a manual transmission, and the car is available in one of four colors. Relevant probabilities for various combinations of transmission type and color are given in the accompanying table. Color Transmission Type White Blue Black Red 10 15 18 Let A- (automatic transmission, B- (black), and C- (white. a calculate PA), PLB), and PA n B). D. Calculate both PA / B) and PBA, and explain in context what each of these probabilities represents. C. Are the events "Automatic transmission" and "Black" independent? Justify your answer 1. A chemical supply company currently has in stock 100 lb of a certain chemical, which it sells to customers in St atches. Let X- the number of batches ordered by a randomly chosen customer and suppose that X has put Compute the expected number of batches ordered

Explanation / Answer

Q5.

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 * 0.2
= 2
II.
variance = npq
where
n = total number of repetitions experiment is excueted
p = success probability
q = failure probability
variance = 10 * 0.2 * 0.8
= 1.6
III.
standard deviation = sqrt( variance ) = sqrt(1.6)
=1.2649
a.
P( X < = 4) = P(X=4) + P(X=3) + P(X=2) + P(X=1) + P(X=0)
= ( 10 4 ) * 0.2^4 * ( 1- 0.2 ) ^6 + ( 10 3 ) * 0.2^3 * ( 1- 0.2 ) ^7 + ( 10 2 ) * 0.2^2 * ( 1- 0.2 ) ^8 + ( 10 1 ) * 0.2^1 * ( 1- 0.2 ) ^9 + ( 10 0 ) * 0.2^0 * ( 1- 0.2 ) ^10
= 0.9672
b.
P( X = 3 ) = ( 10 3 ) * ( 0.2^3) * ( 1 - 0.2 )^7
= 0.2013
c.
P( X < 3) = P(X=2) + P(X=1) + P(X=0)   
= ( 10 2 ) * 0.2^2 * ( 1- 0.2 ) ^8 + ( 10 1 ) * 0.2^1 * ( 1- 0.2 ) ^9 + ( 10 0 ) * 0.2^0 * ( 1- 0.2 ) ^10
= 0.6778
P( X > = 3 ) = 1 - P( X < 3) = 0.3222

d.
the no.of 10 drivers expect to complete stop = mean = np
where
n = total number of repetitions experiment is excueted
p = success probability
mean = 10 * 0.2
= 2

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