Get the answers you need at Westonci.ca, where our expert community is dedicated to providing you with accurate information. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
Answer:
A. 0.33496 = 33.496% probability that one out of the next four cars needs oil.
B. 0.19635 = 19.635% probability that two out of the next eight cars needs oil.
C. 0.01437 = 1.437% probability that 10 out of the next 40 cars needs oil.
Step-by-step explanation:
For each customer, there are only two possible outcomes. Either their car needs to have oil added, or it does not. The probability of a customer having a car needing oil addition is independent of any other customer. This means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
One out of 8 cars needs to have oil added.
This means that [tex]p = \frac{1}{8} = 0.125[/tex]
A. One out of the next four cars needs oil.
This is [tex]P(X = 1)[/tex] when [tex]n = 4[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 1) = C_{4,1}.(0.125)^{1}.(0.875)^{3} = 0.33496[/tex]
0.33496 = 33.496% probability that one out of the next four cars needs oil.
B. Two out of the next eight cars needs oil.
This is [tex]P(X = 2)[/tex] when [tex]n = 8[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{8,2}.(0.125)^{2}.(0.875)^{6} = 0.19635[/tex]
0.19635 = 19.635% probability that two out of the next eight cars needs oil.
C. 10 out of the next 40 cars needs oil.
This is [tex]P(X = 10)[/tex] when [tex]n = 40[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 10) = C_{40,10}.(0.125)^{10}.(0.875)^{30} = 0.01437[/tex]
0.01437 = 1.437% probability that 10 out of the next 40 cars needs oil.
We appreciate your time. Please revisit us for more reliable answers to any questions you may have. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.
