Thank you for visiting From past experience a restaurant owner has determined that 40 of those who visit her restaurant will spend at least 125 If 8 people will. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
The probability that exactly four people will spend at least $125, using the binomial distribution, is of:
0.2322 = 23.22%.
What is the binomial distribution formula?
The mass probability formula, used to obtain the probability of x successes, is of:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are given as follows:
- n is the number of trials of the experiment.
- p is the probability of a success on a single trial of the experiment.
The values of these parameters in this problem are given as follows:
- n = 8, as 8 people will visit her restaurant tomorrow.
- p = 0.4, as 40% of those who visit her restaurant will spend at least $125.
The probability that exactly four people will spend at least $125 is P(X = 4), hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 4) = C_{8,4}.(0.4)^{4}.(0.6)^{4} = 0.2322[/tex]
More can be learned about the binomial distribution at https://brainly.com/question/24756209
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