Looking for answers? Westonci.ca is your go-to Q&A platform, offering quick, trustworthy responses from a community of experts. Explore in-depth answers to your questions from a knowledgeable community of experts across different fields. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.
Sagot :
Answer:
0.9452 = 94.52% probability that more than 3 adults in the sample prefer saving over spending
Step-by-step explanation:
For each adult, there are only two possible outcomes. Either they prefer saving over spending, or they do not. The answers for each adult are independent, which 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.
According to a Gallup poll, 60% of American adults prefer saving over spending.
This means that [tex]p = 0.6[/tex]
Sample of 10 American adults
This means that [tex]n = 10[/tex]
What is the probability that more than 3 adults in the sample prefer saving over spending?
This is:
[tex]P(X > 3) = 1 - P(X \leq 3)[/tex]
In which
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{10,0}.(0.6)^{0}.(0.4)^{10} = 0.0001[/tex]
[tex]P(X = 1) = C_{10,1}.(0.6)^{1}.(0.4)^{9} = 0.0016[/tex]
[tex]P(X = 2) = C_{10,2}.(0.6)^{2}.(0.4)^{8} = 0.0106[/tex]
[tex]P(X = 3) = C_{10,3}.(0.6)^{3}.(0.4)^{7} = 0.0425[/tex]
Then
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0001 + 0.0016 + 0.0106 + 0.0425 = 0.0548[/tex]
[tex]P(X > 3) = 1 - P(X \leq 3) = 1 - 0.0548 = 0.9452[/tex]
0.9452 = 94.52% probability that more than 3 adults in the sample prefer saving over spending
We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.
