The industry standards suggest that 20% of new vehicles require warranty service
ID: 3387875 • Letter: T
Question
The industry standards suggest that 20% of new vehicles require warranty service within the first year. A dealer sold 20 Nissans yesterday. Use equation for Binomial Probability for part a) and Table II for part b) & c). Show work! What is the probability that none of these vehicles requires warranty service? Use the Binomial equation for P(X=0). What is the probability that exactly one of these vehicles requires warranty service? Determine the probability 3 or more of these vehicles require warranty service. Compute the mean and std. dev. of this probability distribution.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 = 20
p = the probability of a success = 0.2
x = the number of successes = 0
Thus, the probability is
P ( 0 ) = 0.011529215 [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 = 20
p = the probability of a success = 0.2
x = the number of successes = 1
Thus, the probability is
P ( 1 ) = 0.057646075 [ANSWER]
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c)
Note that P(at least x) = 1 - P(at most x - 1).
Using a cumulative binomial distribution table or technology, matching
n = number of trials = 20
p = the probability of a success = 0.2
x = our critical value of successes = 3
Then the cumulative probability of P(at most x - 1) from a table/technology is
P(at most 2 ) = 0.206084719
Thus, the probability of at least 3 successes is
P(at least 3 ) = 0.793915281 [ANSWER]
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d)
u = mean = np = 4 [ANSWER]
s = standard deviation = sqrt(np(1-p)) = 1.788854382 [ANSWER]
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