Industry standards suggest that 13% of new vehicles require warranty service within the first year. Jones Nissan in Sumter, South Carolina, sold 15 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 µ
Standard deviation ?

Hey this is the solution for 16%, 2 vehicles sold solution. You can plug your values (13%, 15 vehicles) to the below solution to get your answers.

Use the Binomial Probability Distribution Formula:

Probability (P) (k successes in n trials) = nCk * p^(k) * (1-p)^(n-k), where nCk = n! / (k! * (n-k)!):

For these problems n=8 and p=0.16:

a) P (k=0) = 8C0 * (0.16)^0 * (1-0.16)^(8-0) = 0.2479:

b) P (k=1) = 8C1 * (0.16)^1 * (1-0.16)^(8-1) = 0.3777:

c) P (k=2) = 8C2 * (0.16)^2 * (1-0.16)^(8-2) = 0.2518:

d) P (k<3) = P(k=0) +P(k=1) +P(k=2) = 0.2479 +0.3777 +0.2518 = 0.8774:

e. Compute the mean and standard deviation of this probability distribution:

mean = 8 * 0.16 = 1.28:

standard deviation = square root(n * p * (1-p)) = square root(8 * 0.16 * (1-0.16)) = 1.0369

Hope it helps.