An automobile service facility specializing in engine tuneup

An automobile service facility specializing in engine tune-ups knows that 45% of all tune-ups are done on four-cylinder automobiles, 40% on six-cylinder automobiles, and 15% on eight-cylinder automobiles. Let

X = the number of cylinders on the next car to be tuned.(a) What is the pmf of X?

(b) Draw a line graph for the pmf of part (a).

Draw a probability histogram for the pmf of part (a).

(c) What is the probability that the next car tuned has at least six cylinders?


What is the probability that the next car tuned has more than six cylinders?

Solution

a)

x .........4 ......6 ......8

p(x) .....0.45....0.4.....0.15

b)

the correct graph representing above distribution is

first graph

correct histogram representing the pmf

is second histogram

c)

probability that it has atleast six cylinders

P(x>=6) = P(X=6) + P(X=8) = 0.40 + 0.15 = 0.55

probability that it as more than 6 cylinders

P(X>6) = P(X=8)

=0.15