Question

25, Industry standards suggest that 10% of new vehicles require warranty service within the first year. Jones Nissan in Sumter, South Carolina, sold 12 Nissans yesterday (a) What is the probability that none of these vehicles requires warranty service?(Round your answer to 4 decimal places.) Probability (b) What is the probability exactly one of these vehicles requires warranty service? (Round your answer to 4 decimal places.) Probability (c) Determine the probability that exactly two of these vehicles require warranty service. (Round your answer to 4 decimal places.) Probability (d) Compute the mean and standard deviation of this probability distribution. (Round your answers to 2 decimal places.) Mean Standard deviation ơ

Answer 1

Here we see that n=12 is constant, p=0.10 is same for all, events are independent and only two outcomes

So distribution is binomial $P(x)=\binom{n}{x}p^x(1-p)^{(n-x)}$

a. $P(x=0)=BINOMDIST(0,12,0.1,0)=0.2824$

b. $P(x=1)=BINOMDIST(1,12,0.1,0)=0.3766$

c. $P(x=2)=BINOMDIST(2,12,0.1,0)=0.2301$

d. Mean= $\mu=np=12*0.10=1.2$

Standard deviation is $\sigma=\sqrt{npq}=1.0392$