Of students ages 16 to 18 with A or B average who plan to attend college after g
ID: 3131470 • Letter: O
Question
Of students ages 16 to 18 with A or B average who plan to attend college after graduation, 78% cheated to get higher grades. Ten randomly chosen students with A or B averages who plan to attend college after graduation were asked, "Did you cheat to get higher grades?" What is the probability that exactly 2 students answered no?
a) decide which probability distribution - binomial or poisson - applies to the question. give reason for your answer.
b) State the variable of interest, and the possible values of the variable
c) Find the required probability
Explanation / Answer
A)
We use a binomial distirbution, as the probability of success is 78%, and it is quite high, so we cannot use Poisson Distribution. Also, it satisfies all requirements for the Binomial Distribution.
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b)
We are interested in the number of students who cheated to get higehr grades. The possible values are {0,1,2,3,4,5,6,7,8,9,10}, as our sample only has 10 participants.
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c)
Here, we want the probability that exactly 2 out of the 10 sampled students DID NOT cheat to get higher grades. Hence, 8 out of 10 cheated.
Note that the probability of x successes out of n trials is
P(n, x) = nCx p^x (1 - p)^(n - x)
where
n = number of trials = 10
p = the probability of a success = 0.78
x = the number of successes = 8
Thus, the probability is
P ( 8 ) = 0.29841091 [ANSWER]
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