At Westonci.ca, we connect you with experts who provide detailed answers to your most pressing questions. Start exploring now! Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
Sagot :
Using the binomial distribution, there is a 0.9983 = 99.83% probability that at most eleven of the thirteen babies are girls.
What is the binomial distribution formula?
The formula is:
[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:
- x is the number of successes.
- n is the number of trials.
- p is the probability of a success on a single trial.
For this problem, the values of the parameters are:
p = 0.5, n = 13
The probability that at most eleven of the thirteen babies are girls is:
[tex]P(X \leq 11) = 1 - P(X > 11)[/tex]
In which
P(X > 11) = P(X = 12) + P(X = 13)
Then:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 12) = C_{13,12}.(0.5)^{12}.(0.5)^{1} = 0.0016[/tex]
[tex]P(X = 13) = C_{13,13}.(0.5)^{13}.(0.5)^{0} = 0.0001[/tex]
So:
P(X > 11) = P(X = 12) + P(X = 13) = 0.0016 + 0.0001 = 0.0017
[tex]P(X \leq 11) = 1 - P(X > 11) = 1 - 0.0017 = 0.9983[/tex]
0.9983 = 99.83% probability that at most eleven of the thirteen babies are girls.
More can be learned about the binomial distribution at https://brainly.com/question/24863377
#SPJ1
We hope this was helpful. Please come back whenever you need more information or answers to your queries. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.
