Question

2. In a southern state, it was revealed that 5% of all automobiles in the state did not pass inspection. Of the next ten automobiles entering the inspection station, a what is the probability that none will pass inspection? b. what is the probability that all will pass inspection? c. what is the probability that exactly two will not pass inspection? d. what is the probability that more than three will not pass inspection? e. what is the probability that fewer than two will not pass inspection? f Find the expected number of automobiles not passing inspection. gDetemine the standard deviation for the number of cars not passing inspection

Answer 1

Solution:

Given in the question

n = 10, p= 0.05

Solution(a)

P(X=0) = 10C0*(0.05)^0*(0.95)^10 = 0.5987

Solution(b)

P(X=10 will pass) = 10C10*(0.95)^10*(0.05)^0 = 0.5987

Solution(c)

P(X=2) = 10C2*(0.05)^2*(0.95)^8 = 0.0746

Solution(d)

P(X>3) = 1- P(X<=3) = 1 - P(X=0) - P(X=1) -P(X=2) - P(X=3) = 1- 10C0*(0.05)^0*(0.95)^10-10C1*(0.05)^1*(0.95)^9-10C2*(0.05)^2*(0.95)^8-10C3*(0.05)^3*(0.95)^7 = 1 - 0.5987 - 0.3151 - 0.0746 - 0.0105 = 0.0011

Solution(e)

P(X<2) = P(X=0) +P(X=1) = 10C0*(0.05)^0*(0.95)^10 + 10C1*(0.05)^1*(0.95)^9 = 0.5987 + 0.3151 = 0.9139

Solution(f)

Expected number of automobiles not passing inspection = n*p = 10*0.05 = 0.5

Solution(g)

Standard deviation = sqrt(n*p*q) = sqrt(10*0.05*0.95) = 0.6892