Question

Industry standards suggest that 13 percent of new vehicles require warranty service within the first year. Jones Nissan in Sumter, South Carolina, sold 12 Nissans yesterday. (Round your mean answer to 2 decimal places and the other answers to 4 decimal places.) What is the probability that none of these vehicles requires warranty service

Answer 1

Answer: 0.1880

Explanation:

The binomial distribution formula is given by :-

`P(x)=^nC_xp^x(1-p)^(n-x)`

where P(x) is the probability of x successes out of n trials, p is the probability of success on a particular trial.

Given : The probability of new vehicles require warranty service within the first year : p =0.13.

Number of trials : n= 12

Now, the required probability will be :

`P(x=0)=^(12)C_0(0.13)^(0)(1-0.13)^(12-0)\\\\=(1)(0.13)^(0)(0.87)^(12)=0.188031682201\approx0.1880`

Thus, the probability that none of these vehicles requires warranty service = 0.1880