1.) Consider a binomial distribution with 8 trials. Look at a binomial probabili
ID: 3328812 • Letter: 1
Question
1.) Consider a binomial distribution with 8 trials. Look at a binomial probability distribution table showing binomial probabilities for various values of p, the probability of success on a single trial.
(a) For what value of p is the distribution symmetric?
p =
What is the expected value of this distribution?
2.) In the book A Guide to the Development and Use of the Myers-Briggs Type Indicators by Myers and McCaully, it was reported that approximately 45% of all university professors are extroverted. Suppose you have classes with three different professors.
a.) What is the probability that at least two of your professors are extroverts? (Round your answer to three decimal places.)
b.) In a group of three professors selected at random, what is the expected number of extroverts? (Round your answer to two decimal places.)
_________ extroverts
What is the standard deviation of the distribution? (Round your answer to two decimal places.)
______ extroverts
c.) Suppose you were assigned to write an article for the student newspaper and you were given a quota (by the editor) of interviewing at least three extroverted professors. How many professors selected at random would you need to interview to be at least 89% sure of filling the quota?
______ professors
3.) Consumer Banker Association released a report showing the lengths of automobile leases for new automobiles. The results are as follows.
- Use the midpoint of each class, and call the midpoint of the last class 66.5 months, for purposes of computing the expected lease term. Also find the standard deviation of the distribution. (Round your answers to two decimal places.)
4.)In Hawaii shark attacks are very rare. Furthermore, about 55% of all shark attacks are serious, but not fatal.† You are scheduled to give a talk at a local scuba club in Honolulu and want to include a brief statistical profile regarding the most recent seven shark attacks, all of which were nonfatal. Let r be the number of nonfatal attacks out of a random sample of seven shark attacks.
a.) What is the probability all seven shark attacks are nonfatal? (Round your answer to three decimal places.)
b.) What is the probability that three or more of the seven shark attacks are nonfatal? (Round your answer to three decimal places.)
c.) What is the expected number of nonfatal shark attacks out of the seven?
What is the standard deviation of the r-probability distribution? (Round your answer to three decimal places.)
25-36
37-48
49-60
More than 60 10.9%
39.1%
25.9%
23.9%
0.2%
Explanation / Answer
1.) Consider a binomial distribution with 8 trials. Look at a binomial probability distribution table showing binomial probabilities for various values of p, the probability of success on a single trial.
(a) For what value of p is the distribution symmetric?
p = 0.5
What is the expected value of this distribution?
E(x) = 8 * 0.5 = 4
2.) In the book A Guide to the Development and Use of the Myers-Briggs Type Indicators by Myers and McCaully, it was reported that approximately 45% of all university professors are extroverted. Suppose you have classes with three different professors.
a.) What is the probability that at least two of your professors are extroverts? (Round your answer to three decimal places.)
P( X >=2) = P(X =2) + P(X =3) = 3C2(0.45)2 (0.55) + 3C3(0.45)3 = 0.4253
b.) In a group of three professors selected at random, what is the expected number of extroverts? (Round your answer to two decimal places.)
_________ extroverts
E(X) = 3 * 0.45 = 1.35
What is the standard deviation of the distribution? (Round your answer to two decimal places.)
STD(X) = Sqrt [ 3 * 0.45 * 0.55] = 0.8617 extroverts
c.) Suppose you were assigned to write an article for the student newspaper and you were given a quota (by the editor) of interviewing at least three extroverted professors. How many professors selected at random would you need to interview to be at least 89% sure of filling the quota?
______ professors
as we can apply chebhesyev's inequality. For 89% sureness, we have to take atleast mean +- 3 standard deviation.
Pr(X >=3 ; n ; 0.45) > 0.89
Pr( X = 0,1,2 ; n ; 0.45) < 0.11
nC0 (0.55)n + nC1 (0.55)n-1(0.45) + nC2(0.55)n-2(0.45)2 < 0.11
so n here = 10
n = 10 professors
3.) Consumer Banker Association released a report showing the lengths of automobile leases for new automobiles. The results are as follows.
4.)In Hawaii shark attacks are very rare. Furthermore, about 55% of all shark attacks are serious, but not fatal.† You are scheduled to give a talk at a local scuba club in Honolulu and want to include a brief statistical profile regarding the most recent seven shark attacks, all of which were nonfatal. Let r be the number of nonfatal attacks out of a random sample of seven shark attacks.
a.) What is the probability all seven shark attacks are nonfatal? (Round your answer to three decimal places.)
= 7C7 * (0.45)7 = 0.0037
b.) What is the probability that three or more of the seven shark attacks are nonfatal? (Round your answer to three decimal places.)
Pr( X >=3 ; 7; 0.55) = 1 - [Pr(X= 0) + Pr( X = 1) + Pr( X = 2)]
= 1 - 0.1529 = 0.8471
c.) What is the expected number of nonfatal shark attacks out of the seven?
E(X) = 7 * 0.55 = 3.85
What is the standard deviation of the r-probability distribution? (Round your answer to three decimal places.)
STD(X) = Sqrt [7 * 0.55 * 0.45] = 1.316
Lease month(x) Percent lease p(x) xp(x) p(x) * (x - xo)^2 18.5 0.109 2.0165 41.90763 30.5 0.391 11.9255 22.63173 42.5 0.259 11.0075 4.996023 54.5 0.239 13.0255 64.21874 66.5 0.002 0.133 1.612211 sum 1 38.108 135.3663Related Questions
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