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3 Problem set for Section 3.3 Binomial Distributions 1. For the following experiments, determine if the trial results in a binomial distribution. If so, specify the parameters p and n. If not, briefly explain how the model fails to meet a condition of binomial distributions. (a) Surveying 12 jurors and recording whether there is a "no" response when they are asked if they have ever been convicted of a felony (b) Recording the number of children in 250 families (c) Surveying 250 married couples and recording whether there is a "yes" response when they are asked if they have any children 2. Jacob Elordi takes a statistics exam without studying first. The exam is 12 questions long, each of a true/false format. He decides to randomly guess on all the questions. (a) If we model the number of correct answers on Jacob Elordi's exam as a binomial distribution, what are the parameters p and n? (b) Find the probability that he gets exactly 6 right. (c) Find the probability that he gets no more than 4 right. (d) Find the probability that he manages to guess them all correctly. 3. It's estimated that 18% of U.S. seniors aged 60 and above have cataracts (American Academy of Opthamology, 2023). In a clinical trial, 20 seniors undergo eye exams and the opthamologist deter- mines the number of seniors in the trial who have cataracts. (a) Is it valid to model this with a binomial distribution? Briefly explain why or why not, and if so, provide the parameters p and n. (b) Assume X has a binomial distribution. What is the expected number of seniors in the trial who have cataracts? (c) It's determined that 17 out of 20 seniors have cataracts. Is this considered a significantly high outcome by the Strong Range Rule of Thumb for Random Variables?

Name: 3 problem set for section 33 binomial distributions 1 for the following experiments determine if the trial results in a binomial distribution if so specify the parameters p and n if not brie 78147
Uploaded: 2022-03-21T03:49:49-08:00
Duration: 2 min 46 s
Channel: Manisha Sarker
Description: 3 problem set for section 33 binomial distributions 1 for the following experiments determine if the trial results in a binomial distribution if so specify the parameters p and n if not brie 78147

3 Problem set for Section 3.3 Binomial Distributions
1. For the following experiments, determine if the trial results in a binomial distribution. If so, specify
the parameters p and n. If not, briefly explain how the model fails to meet a condition of binomial
distributions.
(a) Surveying 12 jurors and recording whether there is a "no" response when they are asked if they
have ever been convicted of a felony
(b) Recording the number of children in 250 families
(c) Surveying 250 married couples and recording whether there is a "yes" response when they are
asked if they have any children
2. Jacob Elordi takes a statistics exam without studying first. The exam is 12 questions long, each of a
true/false format. He decides to randomly guess on all the questions.
(a) If we model the number of correct answers on Jacob Elordi's exam as a binomial distribution,
what are the parameters p and n?
(b) Find the probability that he gets exactly 6 right.
(c) Find the probability that he gets no more than 4 right.
(d) Find the probability that he manages to guess them all correctly.
3. It's estimated that 18% of U.S. seniors aged 60 and above have cataracts (American Academy of
Opthamology, 2023). In a clinical trial, 20 seniors undergo eye exams and the opthamologist deter-
mines the number of seniors in the trial who have cataracts.
(a) Is it valid to model this with a binomial distribution? Briefly explain why or why not, and if so,
provide the parameters p and n.
(b) Assume X has a binomial distribution. What is the expected number of seniors in the trial who
have cataracts?
(c) It's determined that 17 out of 20 seniors have cataracts. Is this considered a significantly high
outcome by the Strong Range Rule of Thumb for Random Variables?

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