ECON1030 Chapter Notes - Chapter 6: Binomial Distribution
6.48) Probability of obtaining at least 50% in the examination = 0.0006 approx.
6.50)
a) Probability that the age of a randomly chosen house in New Acres is more than 30 years = 0.5
b) Probability that the age of a randomly chosen house in New Acres is between 25 and 35 years =
0.5
c) Probability that the age of a randomly chosen house in New Acres is less than 35 years = 0.75
Explanation:
6.48)
Total number of questions, n = 40
Each question having four options.
Probability of a correct answer, p = 0.25 ......(i.e. 1/4)
Probability of wrong answer, q = 0.75
Probability of obtaining at least 50% in the examination:
One can obtain 50% in the exam after answering 20 question correct out of 40 questions. It
means one has to correctly answer atleast 20 questions out of 40 questions to obtain atleast 50%
in the exam.
As per Binomial distribution:
P(X=r)=Crnprqn−r
Crn=r!(n−r)!n!
Let, X represents the number of questions answered correct.
Probability of answering atleast 20 questions correct i.e. P(X ≥ 20)
P(X ≥ 20) = P(X = 20) + P(X = 21) + ....................+ P(X = 39) + P(X = 40)
Using Excel:
P(X ≥ 20) = 0.000572
Use excel function: =1-BINOMDIST(20, 40, 0.25, 1)+ BINOMDIST(20, 40, 0.25, 0)
Therefore,
Probability of obtaining at least 50% in the examination = 0.0006 approx.
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Document Summary
6. 48) probability of obtaining at least 50% in the examination = 0. 0006 approx. 0. 5: probability that the age of a randomly chosen house in new acres is less than 35 years = 0. 75. Probability of a correct answer, p = 0. 25 (i. e. 1/4) Probability of obtaining at least 50% in the examination: One can obtain 50% in the exam after answering 20 question correct out of 40 questions. It means one has to correctly answer atleast 20 questions out of 40 questions to obtain atleast 50% in the exam. Let, x represents the number of questions answered correct. Probability of answering atleast 20 questions correct i. e. p(x 20) P(x 20) = p(x = 20) + p(x = 21) + + p(x = 39) + p(x = 40) Use excel function: =1-binomdist(20, 40, 0. 25, 1)+ binomdist(20, 40, 0. 25, 0) Probability of obtaining at least 50% in the examination = 0. 0006 approx.
