Please show all steps. 3. In a southern state, it was revealed that 5% of all au

Question

Please show all steps.

3. In a southern state, it was revealed that 5% of all automobiles in the state did not pass inspection. What is the probability that of the next ten automobiles entering the inspection station a. None will pass inspection? b. All will pass inspection? c. Exactly two will not pass inspection? e. More than three will not pass inspection? f. Less than two will not pass inspection? g. Find the expected number of automobiles not passing inspection. h. Determine the standard deviation for the number of cars not passing inspection.

Explanation / Answer

P(not pass the inspection) = 0.05

P(pass the inspection) = 1- 0.05 = 0.95

n = 10

A) P(x = 0) = 10C0 * (0.05)0 * (1 - 0.05)10 - 0

= 1 * 1 * (0.95)10 = 0.6

B) P(X = 10) = 10C10 * (0.95)10 * (0.05)0 = 0.6

C) P(x = 2) = 10C2 * (0.05)2 * (0.95)8 = 0.075

E) P(x < 3) = P(x = 0) + P(X = 1) + P(x = 2) + P(x = 3)

= 10C0 * (0.95)0 * (0.05)10 + 10C1 * (0.95)1 * (0.05)9 +10C2 * (0.95)2 * (0.05)8 + 10C3 * (0.95)3 * (0.05)7 = 0.0000001

F) P(x < 2) = P(x = 0) + P(x = 1)

= 10C 0 * (0.05)0 (0.95)10 + 10C1 * (0.05)1 * (0.95)9 = 0.6 + 0.32 = 0.92

G) expected no of automobile not passing inspection = 10 * 0.05 = 0.5

H) standard deviation for no of cars not passing inspection = sqrt(10 * 0.05 * 0.95) 2.18

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