Industry standards suggest that 10% of new vehicles ...
Industry standards suggest that 10% of new vehicles require warranty service within the 1st year. Jackson Chevy in Detroit, MI, sold 12 cars yesterday. a. What is the probability that none of these cars requires warranty service? b. What is the probability exactly 1 of these vehicles requires warranty service? c. Determine the probability that exactly 2 of these vehicles require warranty service? d. Compute the mean and standard deviation of this probability distribution.
Let X denote the number of vehicles requires warranty service among the sold 12 cars. Then X can take the values 0,1,2,…,12. Also it is given that the probability of new vehicles require warranty service is 0.10. Thus clearly X follows a Binomial distribution with parameters n = 12 and p = 0.10.
Now the probability distribution of X is
[pic], [pic]
a) The probability that none of these cars requires warranty service is given by
[pic]=[pic] = 0.28243
b) The probability exactly 1 of these vehicles requires warranty service is given by
[pic] = 12*0.10*(0.90)11 = 0.37657
c) The probability that exactly 2 of these vehicles require warranty service is given by,
[pic] = 66*(0.10)2*(0.90)10 = 0.23013
d) For a binomial distribution with parameters n and p, the mean and standard deviations are np and [pic]respectively.
Thus, Mean = np = 12*0.10 = 1.2
Standard Deviation = [pic]=[pic]=1.03923
Note that the binomial probability P[X = x] can be determined using the Excel function =BINOMDIST(x ,12,0.10,0)
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