Question

(1 point) A sign on the pumps at a gas station encourages customers to have their oil checked, and claims that one out of 5 cars needs to have oil added. If this is true, what is the probability of each of the following: A. Exactly three out of the next eight cars needs oil. Probability = B. At least three out of the next eight cars needs oil. Probability = C. At most 6 out of the next 8 cars needs oil. Probability =

          (1 point)
A sign on the pumps at a gas station encourages customers to have their oil checked, and claims that one out of 5 cars needs to have oil added.
If this is true, what is the probability of each of the following:
A. Exactly three out of the next eight cars needs oil.
Probability =
B. At least three out of the next eight cars needs oil.
Probability =
C. At most 6 out of the next 8 cars needs oil.
Probability =

Show more…

1 point a sign on the pumps at a gas station encourages customers to have their oil checked and claims that one out of 5 cars needs to have oil added if this is true what is the probability 51171

Added by Natasha P.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Audrey Fong

05/09/2022

Step 1

The probability that a car needs oil added is $p = \frac{1}{5} = 0.2$. The number of cars is $n = 8$. This is a binomial distribution with parameters $n=8$ and $p=0.2$. The probability mass function is given by: $P(X=k) = \binom{n}{k} p^k (1-p)^{n-k} = Show more…

Show all steps

lock

Thanks for your feedback!

(1 point) A sign on the pumps at a gas station encourages customers to have their oil checked, and claims that one out of 5 cars needs to have oil added. If this is true, what is the probability of each of the following: A. Exactly three out of the next eight cars needs oil. Probability = B. At least three out of the next eight cars needs oil. Probability = C. At most 6 out of the next 8 cars needs oil. Probability =

Play audio

Feedback

Powered by NumerAI

Audrey Fong and 86 other subject Intro Stats / AP Statistics educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Recommended Videos

Recommended Textbooks

Transcript

00:01 In this question, we're given a gas station claims that one out of three cars needs to have oil added, and we'll assume the claim is true.

00:09 Now, the next eight cars are considered.

00:12 I'm going to let x be the number of cars out of eight that needs oil.

00:16 Now, x follows the binomial distribution, of which there are four criterias.

00:20 First criteria, the number of trials, n is fixed and are identical.

00:24 In this case, there are eight cars, so n is eight.

00:27 So there are eight trials.

00:28 This trial is looking at a car, whether it needs.

00:30 Needs oil or not.

00:31 So the trials are all identical.

00:35 So the first criteria is fulfilled.

00:37 Second criteria, each trial is independent.

00:39 So each car, whether they need oil or not is independent on the other cars.

00:44 So second criteria is fulfilled.

00:46 Third criteria, each trial results in one and two outcomes, success and failure.

00:50 Now the success would be the cars need oil, a car needs oil.

00:54 The failure will be a car does not need oil.

00:56 So the third criteria is fulfilled.

00:58 Fourth the fourth criteria is the probability of success denoted by p remains the same from trial to trial.

01:04 In this case, probability of a single trial is probability of a car -needing oil, and there is one out of three, or p is one -third...

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later