In a southern state, it was revealed that 5% of all automobiles in the state did
ID: 3150093 • Letter: I
Question
In a southern state, it was revealed that 5% of all automobiles in the state did not pass emissions testing. Suppose we look at the next ten (10) automobiles entering the emissions station. Assume that passing emissions test for each automobile is independent.
What is the probability that at least one will not pass the emissions testing?
What is the probability that exactly two will not pass emissions testing?
Find the expected number of automobiles not passing emissions testing, µX.
Determine the standard deviation for the number of cars not passing emissions testing, X.
Explanation / Answer
A)
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 = 0.05
x = the number of successes = 0
Thus, the probability is
P ( 0 ) = 0.598736939
Thus,
P(at least one) = 1 - P(0) = 0.401263061 [ANSWER]
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b)
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 = 0.05
x = the number of successes = 2
Thus, the probability is
P ( 2 ) = 0.074634799 [ANSWER]
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c)
Hence,
u = mean = np = 0.5 [ANSWER]
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d)
Also,
s = standard deviation = sqrt(np(1-p)) = 0.689202438 [ANSWER]