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sveticcg [70]
3 years ago
7

The distribution of speeds on a particular highway has a mean of 60 mph with a standard deviation of 10 mph. The distribution of

speeds is NOT known to be bell-shaped. Use the scenario to answer the next 3 questions.
At least what percentage of cars is traveling between 40 and 80 mph?

At least what percentage of cars is traveling between 20 and 100 mph?

If a sample of 40 cars is selected at random, estimate the number of cars that are traveling between 40 and 80 mph.
Mathematics
1 answer:
PSYCHO15rus [73]3 years ago
5 0

Answer:

a) At least what percentage of cars is traveling between 40 and 80 mph?

75%

b) At least what percentage of cars is traveling between 20 and 100 mph?

93.75%

c) If a sample of 40 cars is selected at random, estimate the number of cars that are traveling between 40 and 80 mph.

30 cars.

Step-by-step explanation:

We apply Chebyshev's Theorem

This states that:

1) At least 3/4 (75%) of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ.

2) At least 8/9 (88.89%) of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ.

3) At least 15/16 (93.75%) of data falls within 4 standard deviations from the mean - between μ - 4σ and μ + 4σ.

From the question, we have:

Mean of 60 mph

Standard deviation of 10 mph.

a) At least what percentage of cars is traveling between 40 and 80 mph?

Applying:

Applying the first rule: At least 3/4 (75%) of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ.

μ – 2σ

60 - 2(10)

60 - 20

= 40 mph

μ + 2σ.

60 + 2(10)

60 + 20

= 80 mph

Hence, at least 75% of cars is traveling between 40 and 80 mph.

b) At least what percentage of cars is traveling between 20 and 100 mph?

At least 15/6 (93.75%) of data falls within 4 standard deviations from the mean - between μ – 4σ and μ + 4σ.

μ – 4σ

60 - 4(10)

60 - 40

= 20 mph

μ + 4σ.

60 + 4(10)

60 + 40

= 100 mph

Hence, at least 93.75% of cars is traveling between 40 and 80 mph.

c) If a sample of 40 cars is selected at random, estimate the number of cars that are traveling between 40 and 80 mph.

Since we know from question a) that

at least 75% of cars is traveling between 40 and 80 mph.

Given a sample of 40 cars:

75% of 40 cars

= 75/100 × 40

= 30 cars.

The number of cars that are traveling between 40 and 80 mph is 30 cars.

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PLEASEPLEASE ANSWER
IRINA_888 [86]

Answer:

x = 7

Step-by-step explanation:

A triangle's total interior angle measurement will equal 180°.

Set all measurements equal to 180:

(82) + (9x - 6) + (6x - 1) = 180

Simplify. Combine like terms:

(82 - 6 - 1) + (9x + 6x) = 180

(82 - 7) + (15x) = 180

(75) + 15x = 180

Next, isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operation, and stands for:

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

~

First, Subtract 75 from both sides of the equation:

15x + 75 = 180

15x + 75 (-75) = 180 (-75)

15x = 180 - 75

15x = 105

Next, divide 15 from both sides of the equation:

(15x)/15 = (105)/15

x = 105/15

x = 7

7 is your value for x.

~

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Your answer would be 24 and 168
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