Car color preferences change over the years and according to the particular mode

Question

Car color preferences change over the years and according to the particular model that the customer selects. In a recent year, suppose that 10% of all luxury cars sold were black. If 25 cars of that year and type are randomly selected, find the following probabilities. (Round your answers to three decimal places.)

(a) At least six cars are black.

(b) At most seven cars are black.

(c) More than five cars are black.

(d) Exactly five cars are black.

(e) Between three and six cars (inclusive) are black.

(f) More than 20 cars are not black.

Explanation / Answer

Solution:- p = 0.10 , n = 20
a)P(x > = 6)
= 1 - P(x < 6)
= 1 - [P(x=0) +P(x=1)+ P(x=2)+P(x=3)+P(x=4)+P(x=5) ]

= 1 - 0.9666 =  0.0334

b)  P(x < = 7) = P(x=0) +P(x=1)+ P(x=2)+P(x=3)+P(x=4)+P(x=5)+p(x=6)+p(x=7)

= 0.9977

c)  0.0334

d) 0.0646

Explanation:- x~bin(25,0.1)
P(x) = nCx * p^x * q^(n-x).
d. P(x = 5) = 25c5 *0.1^5 *0.6^20 = 0.0646

e) P(3 <= X <= 6) =  P(x=3)+P(x=4)+P(x=5)+p(x=6)

= 0.2265+0.1384+0.0646+0.0239

=  0.4534

f. P(0 <= X <= 4) = 0.9020

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