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Mumz [18]
3 years ago
13

Suppose that the middle 68% of speeding ticket fines on a highway fall between 93.18 and 118. Give an approximate estimate of th

e standard deviation of the speeding ticket fines. Assume the fine amount has a normal distribution
Mathematics
1 answer:
Anton [14]3 years ago
7 0

Answer:

The approximate estimate of the standard deviation of the speeding ticket fines is of 12.41.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

Middle 68% of speeding ticket fines on a highway fall between 93.18 and 118.

This means that 93.18 is one standard deviation below the mean and 118 is one standard deviation above the mean. That is, the difference between 118 and 93.18 is worth two standard deviations. So

2s = 118 - 93.18

s = \frac{(118 - 93.18)}{2}

s = 12.41

The approximate estimate of the standard deviation of the speeding ticket fines is of 12.41.

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A particle moves on a straight line and has acceleration a(t)=24t+2. Its position at time t=0 is s(0)=3 and its velocity at time
user100 [1]

Answer:

It's position at time t = 5 is 593.

Step-by-step explanation:

The velocity v(t) is the integral of the acceleration a(t)

The position s(t) is the integral of the velocity v(t)

We have that:

The acceleration is:

a(t) = 24t + 2

Velocity:

v(t) = \int {a(t)} \, dt = \int {24t + 2} \, dt = 12t^{2} + 2t + K

K is the initial velocity, that is v(0). Since V(0) = 13, K = 13

Then

v(t) = 12t^{2} + 2t + 13

Position:

s(t) = \int {s(t)} \, dt = \int {12t^{2} + 2t + 13} \, dt = 4t^{3} + t^{2} + 13t + K

Since s(0) = 3

s(t) = 4t^{3} + t^{2} + 13t + 3

What is its position at time t=5?

This is s(5).

s(t) = 4t^{3} + t^{2} + 13t + 3

s(5) = 4*5^{3} + 5^{2} + 13*5 + 3

s(5) = 593

It's position at time t = 5 is 593.

3 0
3 years ago
Solve the equation 4+2|3x+4|=-4
ad-work [718]

Answer:

Value of given expression x is -4

Step-by-step explanation:

Given equation in question;

4 + 2|3x + 4| = -4

Find:

Value of given expression

Computation:

4 + 2|3x + 4| = -4

Using BODMAS rule;

⇒ 4 + 2|3x + 4| = -4

⇒ 2|3x + 4| = - 4 - 4

⇒ 2|3x + 4| = - 8

⇒ |3x + 4| = - 8 / 2

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⇒ x = -12 / 3

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Value of given expression x is -4

8 0
3 years ago
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sveticcg [70]

Answer:

1. 78cm^2

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Step-by-step explanation:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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