Question 1206686: A school newspaper reporter decides to randomly survey 18 students to see if they will attend Tet (Vietnamese New Year) festivities this year. Based on past years, she knows that 22% of students attend Tet festivities. We are interested in the number of students who will attend the festivities.
Find the probability that at most 4 students will attend. (Round your answer to four decimal places.)
Find the probability that more than 3 students will attend. (Round your answer to four decimal places.)
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! as far as i can tell, this is a binomial distribution type of problem.
the formula to use is p(x) = p^x * q^(n-x) * c(n,x).
in this problem:
n is 18
x is 0 to 18
p is .22
q is 1 - p = .78
the total distribution is shown in the attached excel printout.
total probability = 1 as it should be.
it's the sum of the probability for x from 0 to 18.
probability for at most 4 students is the sum of the probability for x from 0 to 4.
probability for greater than 3 students is the sum of the probability for x from 4 to 18.
Answer by ikleyn(52847)  (Show Source):
You can put this solution on YOUR website! .
A school newspaper reporter decides to randomly survey 18 students to see if they will attend Tet
(Vietnamese New Year) festivities this year. Based on past years, she knows that 22% of students
attend Tet festivities. We are interested in the number of students who will attend the festivities.
(a) Find the probability that at most 4 students will attend. (Round your answer to four decimal places.)
(b) Find the probability that more than 3 students will attend. (Round your answer to four decimal places.)
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Using cumulative sums, you can reduce the amount of calculations to minimum and perform them in one line, each.
(a) Using your regular calculator TI-83/84 and its standard function binomcdf
P(at most 4 students attend) = P(0) + P(1) + P(2) + P(3) + P(4) = binomcdf(18, 0.22, 4) = 0.6387.
Or, using Excel standard function BINOM.DIST
P(at most 4 students attend) = P(0) + P(1) + P(2) + P(3) + P(4) = BINOM.DIST(4, 18, 0.22, 1) = 0.6387.
(b) Using your regular calculator TI-83/84 and its standard function binomcdf
P(more than 3 students attend) = 1 - (P(0) + P(1) +P(2) + P3)) = 1 - binomcdf(18,0.22,3) = 1 - 0.4175 = 0.5825.
Or, using Excel standard function BINOM.DIST
P(more than 3 students attend) = 1 - (P(0) + P(1) + P(2) + P(3)) = 1 - BINOM.DIST(3,18, 0.22,1) = 0.5825.
Solved.
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When you solve problems on binomial distributions, use standard function binomcdf and/or BINOM.DIST
where it is applicable to calculate cumulative sums and reduce your calculation work.
These functions were specially developed to reduce and facilitate your computational job.
Using these functions is a sign of your competence in the subject.
Ignoring this technique is the sign of incompetence in the subject.
Do not be an enemy to yourself ( ! )
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