Answered

Explore Westonci.ca, the top Q&A platform where your questions are answered by professionals and enthusiasts alike. Connect with professionals ready to provide precise answers to your questions on our comprehensive Q&A platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

A person with type AB blood can donate red blood cells to people with the same blood type. About 12% of the US population has type AB blood. University High held a blood drive where 50 students donated blood. Part A: What is the probability that exactly 8 of the students had type AB blood? Part B: What is the probability that at least 8 of the students had type AB blood?

Sagot :

Using the binomial distribution, it is found that there is a:

A. 0.1075 = 10.75% probability that exactly 8 of the students had type AB blood.

B. 0.2467 = 24.67% probability that at least 8 of the students had type AB blood.

For each student, there are only two possible outcomes, either they have type AB blood, or they do not. The probability of a student having type AB blood is independent of any other student, hence the binomial distribution is used to solve this question.

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.

In this problem:

  • About 12% of the US population has type AB blood, hence [tex]p = 0.12[/tex].
  • A sample of 50 students is taken, hence [tex]n = 50[/tex].

Item a:

The probability is P(X = 8), hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 8) = C_{50,8}.(0.12)^{8}.(0.88)^{42} = 0.1075[/tex]

0.1075 = 10.75% probability that exactly 8 of the students had type AB blood.

Item b:

The probability is:

[tex]P(X \geq 8) = 1 - P(X < 8)[/tex]

In which:

[tex]P(X < 8) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7)[/tex]

Using a calculator to find each probability, we have that:

[tex]P(X < 8) = 0.7533[/tex]

Then:

[tex]P(X \geq 8) = 1 - P(X < 8) = 1 - 0.7533 = 0.2467[/tex]

0.2467 = 24.67% probability that at least 8 of the students had type AB blood.

You can learn more about the binomial distribution at https://brainly.com/question/24863377

We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.