Question

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.
(1) What is the probability mass function of X ?
(2) Determine the cumulative distribution function of X
(3) Draw the graph of the cumulative distribution function of X

Answer 1

Answer:

sorry.........................

Answer 2

Given :  45% of all tune-  ups are done on four cylinder automobiles, 40% on six-cylinder automobiles, and 15% on  eight-cylinder automobiles.

To Find :  pmf of X

probability that the next car tuned has at least six cylinders

More than six  cylinders

Solution:

45 % = 0.45

40 % = 0.4

15 % = 0.15

PMF - probability mass function

$pX(x)=\begin{cases}0.45 \quad x=\text{4 cylinder}\\0.4 ~ \quad x=\text{ 6 cylinder}\\0.15 \quad x=\text{8 cylinder}\end{cases}$

line graph and a probability histogram for the pmf  attached

probability that the next car tuned has at least 6 cylinders = 6  cylinders +  8 cylinder  0.4 + 0.15 = 0.55

probability that  More than 6  cylinders = probability  8 cylinder = 0.15

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