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 20 cars of that year and type are randomly selected, find the following probabilities. Look up the probability in the binomial probability distribution table. Click the blue part and the table will open or you can use the table given in class. (Enter your answers to three decimal places.)

(a) five or more cars are black.

(b) six or less cars are black.

(c) More than four cars are black.

(d) Exactly four cars are black.

(e) Between three and five cars (inclusive - meaning include three and five) are black.

Answer 1

P(black car), p = 0.10

q = 1 - 0.10 = 0.90

Sample size, n = 20

P{X k) for any value of k can be obtained from standard normal distribution table.

(a) P(5 or more), P(X 5) = 1 - P( X < 5)

= 1 - P(X 4)

= 1 - 0.957

= 0.043

(b) P(6 or less) = P(X 6)

= 0.998

(c) P(more than 4), P(X > 4) = 1 - P(X 4)

= 1 - 0.957

= 0.043

(d) P(exactly 4), P(X = 4) = P(X 4) - P(X 3)

= 0.957 - 0.867

= 0.090

(e) P(between 3 and 5, inclusive), P(3 X 5) = P(X 5) - P(X 2)

= 0.989 - 0.677

= 0.312