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8_murik_8 [283]
2 years ago
9

Assume that police estimate that 30% of drivers do not wear their seatbelts. They set up a safety roadblock, stopping cars

Mathematics
1 answer:
STALIN [3.7K]2 years ago
8 0

Using the binomial distribution, it is found that:

a)

  • The mean is of 12.
  • The variance is of 8.4.
  • The standard deviation is of 2.9.

b) They expect to stop 3.3 cars before finding a driver whose seatbelt is not buckled.

For each driver, there are only two possible outcomes, either they wear their seatbelts, or they do not. The probability of a driver wearing their seatbelt is independent of any other driver, hence, the <em>binomial distribution</em> is used to solve this question.

Binomial probability distribution

Probability of exactly <u>x successes on n repeated trials, with p probability</u>.

The expected value of the binomial distribution is:

E(X) = np

The variance of the binomial distribution is:

V(X) = np(1-p)

The standard deviation of the binomial distribution is:

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

In this problem:

  • 30% of drivers do not wear their seatbelts, hence p = 0.3.
  • They stop 40 cars during the first hour, hence n = 40.

Item a:

E(X) = np = 40(0.3) = 12

V(X) = np(1-p) = 40(0.3)(0.7) = 8.4

\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{40(0.3)(0.7)} = 2.9

Hence:

  • The mean is of 12.
  • The variance is of 8.4.
  • The standard deviation is of 2.9.

Item b:

The <u>number of trials until q successes of a binomial variable</u> is modeled by a geometric distribution, with expected value given by:

E(X) = \frac{q}{p}

In this problem, one success, hence q = 1 and:

E(X) = \frac{q}{p} = \frac{1}{0.3} = 3.3

They expect to stop 3.3 cars before finding a driver whose seatbelt is not buckled.

To learn more about the binomial distribution, you can take a look at brainly.com/question/24863377

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What is the solution to 3(–3x + 9) = −18?
Rus_ich [418]

Answer:

x = 5 (If solved algebraically)

No Solution (If the parentheses are absolute value lines)

Step-by-step explanation:

Result when solving this way: 3|-3x + 9| = -18

1) Divide both sides by 3
|-3x + 9| = -18/3

2) Simplify 18/3 to 6

|-3x + 9| = -6

3)  Break down the problem into these 2 equations.

-3x + 9 = -6

- (-3x + 9) = -6

4) Solve the 1st equation: -3x + 9 = -6

- Subtract 1 from both sides.

-3x = -6 - 9

-Simplify -6 - 9 to -15.

-3x = -15

-Divide both sides by -3.

x = -15/-3

- Two negatives make a positive.

x = 15/3

- Simplify 15/3 to 5.

x = 5

6)  Solve the 2nd equation:  - (-3x+ 9) = -6

1 - Remove parentheses

3x - 9 = -6

2 - Add 9 to both sides

3x = -6 + 9

3 - Simplify -6 + 9 to 3.

3x = 3

- Divide both sides by 3.

x = 1

6) Collect all solutions.

x = 1,5

7) Check solution.

When x = 1, the original equation 3|-3x + 9| = -18 does not hold true.

We will drop x = 1 from the solution set.

8) Check solution.

When x = 5, the original equation 3|-3x + 9| = -18  does not hold true.

We will drop x = 5 from the solution set.

9) Therefore,

No solution exists.

Result when solving algebraically:

Simplifying

3(-3x + 9) = -18

Reorder the terms:

3(9 + -3x) = -18

(9 * 3 + -3x * 3) = -18

(27 + -9x) = -18

Solving

27 + -9x = -18

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-27' to each side of the equation.

27 + -27 + -9x = -18 + -27

Combine like terms: 27 + -27 = 0

0 + -9x = -18 + -27

-9x = -18 + -27

Combine like terms: -18 + -27 = -45

-9x = -45

Divide each side by '-9'.

x = 5

Simplifying

x = 5

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Step-by-step explanation:

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Can someone help me with this answer?
Rudik [331]

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I hope I helped you ^_^

3 0
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