Mathematics, 23.04.2020 04:16 gleatons429

Of all the registered automobiles in a city, 8% fail the emissions test. Nine automobiles are selected at random to undergo an emissions test. Round the answers to four decimal places.

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

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 .

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 .

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

Answers: 1

Show answers

Answers

Answer from: antoniocapetillo80

a) The probability that exactly three of them fail the test is 2.61%.

b) The probability that fewer than three of them fail the test is 97.02%.

c) The probability that more than two of them fail the test is 2.98%.

d) It would not be unusual for none of them to fail the test

Step-by-step explanation:

For each automobile, there are only two possible outcomes. Either it fails the test, or it does not. The probability of an automobile faiiling the test is independent of other automobiles. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

8% fail the emissions test.

This means that p = 0.08

Nine automobiles.

This means that n = 9

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

This is P(X = 3)

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 3) = C_{9,3}.(0.08)^{3}.(0.92)^{6} = 0.0261$

The probability that exactly three of them fail the test is 2.61%.

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

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

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{9,0}.(0.08)^{0}.(0.92)^{9} = 0.4722$

$P(X = 1) = C_{9,1}.(0.08)^{1}.(0.92)^{8} = 0.3695$

$P(X = 2) = C_{9,2}.(0.08)^{2}.(0.92)^{7} = 0.1285$

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.4722 + 0.3695 + 0.1285 = 0.9702

The probability that fewer than three of them fail the test is 97.02%.

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

Either fewer than three(two or less) fail, or more than two do. The sum of the probabilities of these events is 100%. So

97.02 + p = 100

p = 2.98

The probability that more than two of them fail the test is 2.98%.

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

More than 2.5 standard deviations from the mean is unusual.

E(X) = np = 9*0.08 = 0.72

$\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{9*0.08*0.72} = 0.81$

0 > 0.72 - 2*0.81

It would not be unusual for none of them to fail the test

Answer from: Quest

x = 25

step-by-step explanation:

a^2+b^2=c^2

7^2+24^2=c^2

49+576=625

sqrt625=25

x=25

What is the value of x? enter your answer in the box. x =

Answer from: Quest

kjgfcvbjkl

step-by-step explanation:

sdfghjkl; vbnm,

Another question on Mathematics

Mathematics, 20.06.2019 18:04

Can someone show me the steps to solve the problem?

Answers: 1

Answer

Mathematics, 21.06.2019 18:50

The first few steps in solving the quadratic equation 9x2 + 49x = 22 ? 5x by completing the square are shown. 9x2 + 49x = 22 ? 5x 9x2 + 54x = 22 9(x2 + 6x) = 22 which is the best step to do next to solve the equation by completing the square? 9(x2 + 6x + 3) = 25 9(x2 + 6x + 3) = 49 9(x2 + 6x + 9) = 31 9(x2 + 6x + 9) = 103

Answers: 3

Answer

Mathematics, 21.06.2019 22:30

Aaron invested a total of $4,100, some in an account earning 8% simple interest, and the rest in an account earning 5% simple interest. how much did he invest in each account if after one year he earned $211 in interest? select one: a. $200 at 8%, $3,900 at 5% b. $3,200 at 8%, $900 at 5% c. $900 at 8%, $3,200 at 5% d. $3,900 at 8%, $200 at 5%

Answers: 1

Answer

Mathematics, 21.06.2019 23:30

If you measured the width of a window in inches and then in feet with measurement would you have the greater number of units

Answers: 3

Answer

You know the right answer?

Of all the registered automobiles in a city, 8% fail the emissions test. Nine automobiles are select...

Questions

Mathematics, 24.11.2021 05:10

Write 2.5kg : 1500g as a ratio in its simplest form...

Mathematics, 24.11.2021 05:10