Question

Car inspection: Of all the registered automobiles in a city,

6%

fail the emissions test. Fifteen automobiles are selected at random to undergo an emissions test. Round the answers to four decimal places.

Part 1 of 4

(a) Find the probability that exactly three of them fail the test.

The probability that exactly three of them fail the test is .

Part 2 of 4

(b) Find the probability that fewer than three of them fail the test.

The probability that fewer than three of them fail the test is .

Part 3 of 4

(c) Find the probability that more than two of them fail the test.

The probability that more than two of them fail the test is .

Part 4 of 4

(d) Would it be unusual for none of them to fail the test?

It ▼(Choose one) be unusual for none of them to fail the test since the probability is .

Answer 1

x = no. of cars that fail

n=15

p = 0.06

1-p = 0.94

a.

P(3) = 15C3 * (0.06^3) * (0.94^(15-3))

= 0.0468

b.

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

= 0.9429

c.

P(x>2) = 1 - P(x<3)

= 1 - 0.9429

= 0.0571

d.

P(none fail) = (1-0.06)^15

= 0.3953

no it wouldn't be unusual as it has more than 5% probability

(please UPVOTE)