Industry standards suggest that 10 percent of new vehicles require warranty serv
ID: 3181138 • Letter: I
Question
Industry standards suggest that 10 percent of new vehicles require warranty service within the first year. Jones Nissan in Sumter, South Carolina, sold 14 Nissans yesterday. (Round your mean answer to 2 decimal places and the other answers to 4 decimal places.)
a. What is the probability that none of these vehicles requires warranty service
b. What is the probability exactly one of these vehicles requires warranty service?
c. Determine the probability that exactly two of these vehicles require warranty service.
d. Compute the mean and standard deviation of this probability distribution.
Industry standards suggest that 10 percent of new vehicles require warranty service within the first year. Jones Nissan in Sumter, South Carolina, sold 14 Nissans yesterday. (Round your mean answer to 2 decimal places and the other answers to 4 decimal places.)
Explanation / Answer
Answers and calculation in detail are as below:
We use the binomial distribution here:
p = .10
n = 14
a. P(X=0) = 14C0 (.1^0)(1-.1)^10 = 0.2288
b. P(X=1) = 14C1 (.1^1)(1-.1)^9 = 0.3559
c. P(X=2) = 14C2 (.1^2)(1-.1)^8 = 0.2570
d. Mean of Binomial dist is given by np = .1*14 = 1.40
Stdev of Binomial dist is given by sqrt(npq) = sqrt(1.4*.9) = 1.1225