Suppose the speeds of cars along a stretch of I-40 is normally distributed with a mean of 70 mph and standard deviation of 5 mph. Use the 68-95-99.7 rule to answer the following questions.
(a) Approximately what percent of cars are travelling between 65 and 75 mph? percent
(b) If the speed limit on this stretch of highway is 65 mph, approximately what percent of cars are traveling faster than the speed limit? percent
(c) What percent of cars are traveling at a speed greater than or equal to 80 mph? (Answer to one decimal place.)
(d) What percent of cars are traveling at a speed greater than 80 mph? (Answer to one decimal place.) percent
(e) 95% of cars are traveling between what two speeds? (Answer to two decimal places) Between mph and mph

Answers

Answer 1

Answer:

a) 68%.

b) 84%.

c) Approximately 2.5% of cars are traveling at a speed greater than or equal to 80 mph.

d) Approximately 2.5% of cars are traveling at a speed greater than or equal to 80 mph.

e) Between 60 mph and 80 mph.

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.

In this problem, we have that:

Mean of 70 mph, standard deviation of 5 mph.

(a) Approximately what percent of cars are travelling between 65 and 75 mph?

70 - 5 = 65

70 + 5 = 75

Within 1 standard deviation, so approximately 68%.

(b) If the speed limit on this stretch of highway is 65 mph, approximately what percent of cars are traveling faster than the speed limit?

The normal distribution is symmetric, which means that 50% of the measures are below the mean, and 50% are above.

65 is one standard deviation below the mean, so of the cars below the mean, 68% are above 65 mph.

0.68*50% + 50% = 34% + 50% = 84%.

84%.

(c) What percent of cars are traveling at a speed greater than or equal to 80 mph?

80 = 70 + 2*10

2 standard deviations above the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean. Due to the symmetry of the normal distribution, of the other 5%, 2.5% is at least 2 standard deviations below the mean and 2.5% is at least 2 standard deviations above the mean. Then:

Approximately 2.5% of cars are traveling at a speed greater than or equal to 80 mph.

(d) What percent of cars are traveling at a speed greater than 80 mph?

Same as item c, as in the normal distribution, the probability of an exact value is considered to be 0.

(e) 95% of cars are traveling between what two speeds?

Within two standard deviations of the mean.

70 - 2*5 = 60 mph

70 + 2*5 = 80 mph.

Between 60 mph and 80 mph.


Related Questions

Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator. 40 gal : 64 gal (IN THE PICTURE)​

Answers

Answer:

5/8

Step-by-step explanation:

The ratio 40:64 can be written as a fraction, 40/64.

Next, simplify to get 5/8.

Hope this helps!

Which ordered pair could be removed from the graph to create a set of ordered pairs that represents a function?

Answers

Answer:

(1,3) hope it helps you good luck

Step-by-step explanation:

Answer:

1,3

Step-by-step explanation:

just took the test on edge

PLEASE ANSWER ASAP!!! FULL ANSWERS ONLY!!!!!! WILL GIVE BRAINLIEST!!!!!!!!!

Two cyclists, 68 miles apart, start riding toward each other at the same time. One cycles 3 miles per hour faster than the other, and they meet after 4 hours of riding.

a. Write an equation using the information as it is given above that can be solved to answer this problem. Use the variable r to represent the speed of the slower cyclist.

b. What are the speeds of the two cyclists? _______________

Answers

Answer:

4r + 4(r + 3) = 68

r = 7 miles per hour

r + 3 = 10 miles per hour

Step-by-step explanation:

distance = rate * time

a)

4r + 4(r + 3) = 68

Distribute

4r + 4r + 12 = 68

8r + 12 = 68

8r = 56

r = 7 miles per hour

r + 3 = 10 miles per hour

a) The given equation using the information as it is given above that can be solved to answer this problem is 4r + 4(r+3) = 68

b) The speed of both cyclists are 3mi/hr and 10mi/hr respectively

The formula for calculating the distance covered is expressed as:

Distance = speed * time

Let the speed covered by one cyclist be t

If one cycles 3 miles per hour faster than the other, the speed of the other will be t + 3

If both meet after 4 hours of riding, then their time will be 4 hours

Distance covered the first cyclist = 4r

Distance covered by the second = 4(r+3)

If the two cyclists are 68 miles apart, then:

4r + 4(r+3) = 68

a) The given equation using the information as it is given above that can be solved to answer this problem is 4r + 4(r+3) = 68

b) Expand the equation in a to get "r"

4r + 4r + 12 = 68

8r + 12 = 68

8r = 68 - 12

8r = 56

r = 56/8

r = 7miles per hour

Speed of the first cyclist = 7mi/hr

Speed of the second cyclist = 3 + 7mi/hr = 10mi/hr

Hence the speed of both cyclists are 3mi/hr and 10mi/hr respectively

Learn more here: https://brainly.com/question/19915685

Plzzzzzz I need in nowwwwwwwwwwww

Answers

Answer:     -5

Step-by-step explanation:

Answer:

b = -5

Step-by-step explanation:

therefore -5 is the answer

The Butlers bought a $332,000 house. They made a down payment of 42,000 and took out a mortgage for the rest. Over the course of 15 years they made monthly payments of $2,447.19 on their mortgage until it was paid off.

(a) What was the total amount they ended up paying for the house (including the down payment and monthly payments)?

(b) How much interest did they pay on the mortgage?

Answers

Answer:

Step-by-step explanation:

(a)Mortgage = 332000 - 42000 = 290000

15 * 12 = 180 months

Total monthly payments = 180 * 2447.19 =440494.2

Total = 440494.2 + 42000 = 482494.2

(b) Interest = 482494.2 -290000

                 = 192494.2

Answer:

a) 482,494.20

b) I'm not sure

Step-by-step explanation:

Can someone please help me with this?? I will like your comment!

Answers

Answer:

[tex]A_{\Delta ABP}=\sin \theta[/tex]

Step-by-step explanation:

Let the center of the circle be O.

Recall that the area of a triangle can be given by:

[tex]\displaystyle A=\frac{1}{2} ab\sin C[/tex]

Where C is the angle between the two sides.

ΔABP is equal to the sum of ΔAPO and ΔBOP.

Let a = OP and b = OB. Since this is the unit circle and PO and BO are radii, they both equal one. C will be θ. Hence, the area of ΔBOP is:

[tex]\displaystyle A_{\Delta BOP}=\frac{1}{2}(1)(1)\sin \theta=\frac{1}{2}\sin\theta[/tex]

For ΔAPO, we can use the two sides OP and OA. Again, they are the radii of the unit circle, so they equal one. The angle in this case will be π - θ radians. Hence:

[tex]\displaystyle A_{\Delta APO}=\frac{1}{2}(1)(1)\sin\left(\pi -\theta\right)=\frac{1}{2}\sin\left(\pi -\theta\right)[/tex]

However, note that sin(π - θ) = sin(θ). Hence:

[tex]\displaystyle A_{\Delta APO}=\frac{1}{2}\sin\left(\theta\right)[/tex]

Hence, the area of ΔABP is:

[tex]\displaystyle A_{\Delta ABP}=\frac{1}{2}\sin \theta+\frac{1}{2}\sin\theta =\sin \theta[/tex]

Which situation would be represented with the integer -72? Select all that apply.

A hike of 72 feet.
A gain of 72 yards, but a loss of 72 yards, ending back at 0.
A withdrawal of 72 dollars.
A height of 72 inches.
A depth of 72 feet.


HELP THIS IS THE LAST TEST OF THE YEAR PLZ HELPP QUICK!!

Answers

Answer:

A withdrawal of 72 dollars & E) a depth of 72 feet

Step-by-step explanation:

It is negative, which means subtract. So we will take away 72 dollars.

A depth of 72 feet is also negative since we are going down.

Which are solution of
[tex] \frac{x}{5} = \frac{1}{x + 4} [/tex]

Answers

X= 1, -5

I’m sorry if it’s not what you’re looking for

Have a good day:)

Answer:

x = 1, x = -5

[tex]x/5 = 1/x+4\\Apply Fraction and Multiply : \\\\x(x+4)=5 x 1\\Simplify :\\x(x+4) = 5\\Solve.[/tex]

I hope this is what you were looking for !

(5x20)+(8x10) PLEASE HELP

Answers

The answer to this equation is 8,000

Answer:

180

Step-by-step explanation:

5*20 is 100. 10 *8 is 80. then you add

Find (f o g)(0) *serious answers only*

Answers

I think the answer should be 0 but I’m not so sure!

answer???
please help

Answers

Answer:

150°

Step-by-step explanation:

M = 58° + 92° (ext angles of a triangle)

M= 150°

Answer:

92+58=1

1=150

measure of angle1 is 150

Select the correct answer from each drop-down menu. In the coming year, a vehicle manufacturer has decided to manufacture 150 vehicles per day. The function v = 150d represents the company’s production for the coming year, v, with respect to the number of days, d. The rate of change of the function representing the number of vehicles manufactured for the coming year is , and its graph is a . So, the function is a function.

Answers

Answer:

Given:

v = 150d

v represents company's production for the coming year

d represents the number of days

150 is the daily production

The rate of change of the function representing the number of vehicles manufactured for the coming year is CONSTANT (150) , and its graph is a STRAIGHT LINE . So, the function is a LINEAR function.

Step-by-step explanation:

please help me pleaseee!!​

Answers

Answer:

AOB = 65

DOE = 35

AOC = 90

EOB = 115

DOB = 80

answer please I’m dying from math

Answers

Step-by-step explanation:

It's C

I hope it helped:)

Can y’all help me on question 31?!

Answers

Answer:

D

Step-by-step explanation:

Area of 1 surface=1×16=16 square units

hence, 16×6=96 square units

Someone please help

Answers

Correct Work

4x+8 +3(x-4)

4x +8 + 3x-12

4x+3x+8 -12

7x -4

Mistake Made

3 wasn't multiplied by the 4 in the bracketLike terms wasn't combined in the working out The answer was supposed to be -4, 8-4= -4

HELPPP I NEED THIS ASAP!!!! What is the next step in the proof? Chose the most logical approach

Answers

I would say D no sure if that’s correct tho

(x – y)(x2 – 3y – 5)

Answers

Solution: ( x - y ) ( 2x - 3y) - 5x + 5y

Which expression is equivalent to the expression -3(4x - 2) - 2x ?

Answers

Answer:

-14x + 6

Step-by-step explanation:

-3(4x - 2) - 2x

-12x + 6 - 2x

-14x + 6

11. Jeff is taking his family and friends to the movies. Adult tickets, a, are $8 and child
tickets, c, are $5. He bought 11 total tickets for $64. Write the system of equations
necessary to compute how many adults and students were in the group.

Answers

Answer:

there are 3 adults and 8 children

Step-by-step explanation:

8*3 (3=Adults)=$24

5*8 (8 children)=$40

24+40=$64

A student is knitting sweaters to give as gifts. The time it takes the student to knit each sweater is 10% less
than the time it took the student to knit each previous sweater. It took the student 14 hours to knit the first
sweater
Which of the following is closest to the time it will take the student to knit the third sweater?
A. 10.2 hours
B. 11.3 hours
C. 12.6hours
D.16.9hours

Answers

Answer:

11 17/50 hours

Step-by-step explanation:

first sweater,

14 hours

second sweater,

14hours × 90%=12 3/5 hours

third sweater,

12 3/5 hours × 90%=11 17/50 hours

11.3 hours is the time taken by the student to knit the third sweater. Option B is correct.

What is Percentage?

percentage, a relative value indicating hundredth parts of any quantity.

Given,

A student is knitting sweaters to give as gifts. The time it takes the student to knit each sweater is 10% less

than the time it took the student to knit each previous sweater. It took the student 14 hours to knit the first

sweater

For first sweater it took 14 hours.

For second sweater it took 10% less time that first sweater

10/100×14=1.4 hrs

14 hrs-1.4 hrs

12.6 hrs.

For second sweater it took 12.6 hours.

For third swaeter it took 10% less time than second sweater.

12.6×0.1=1.26

Now 12.6-1.26=11.3

It took 11.3 hrs for third sweater.

Hence 11.3 hours is the time taken by the student to knit the third sweater. Option B is correct.

To learn more on Percentage click:

https://brainly.com/question/28269290

#SPJ2

Herds of Cattle
P/S R/P Com Con Rep A/Level
Herds of Cattle ○
Rick lives on a large cattle ranch. There has been so little rain that there is not enough grass on parts of the ranch to feed the cattle. Rick needs to move four herds of cattle to be by a river where there is enough grass for the cattle to eat. The river runs through the cattle ranch from point (1, 2) to point (10, 2). The most grass is located at the east end of the river between point (7, 2) and point (10, 2). Plot four new location points where the four herds of cattle can eat the most grass by the river. Show all your mathematical thinking.
First Location of Herds of Cattle
Herd A: (5, 8) Herd B: (2, 9) Herd C: (3, 6) Herd D: (6, 7)

No links please I need this ASAP

Answers

I am also stuck on the same question

Juanita is decorating for a birthday party. She buys more than 30 balloons and attaches 6 of them to the chair for the birthday girl. She also wants to attach balloons to each of the 4 tables, with the same number of balloons at each table. If n represents the number of balloons at each table, this situation can be represented by the inequality 6 + 4n > 30. What does the solution to this inequality represent? A. She must attach fewer than 6 balloons to each table. B. She can attach more than 6 balloons to each table. C. She must attach fewer than 9 balloons to each table. D. She can attach more than 9 balloons to each table

Answers

she can attach 6 balloons to each table making the answer letter A because she must attach less than 6

7.find the equation of a circle with one of the diameters x+2y+8=0and passing through the intersection of a circle x²+y²+2=0 and x²+y²-3y=0.
ans:
[tex]\bold=4x²+4y²+22x+21y=0.}[/tex]​

Answers

Answer:

See below

Step-by-step explanation:

Find the intersection of circles

x² + y² + 2x = 0 and x² + y² - 3y = 0

Subtract the equations to find:

2x = -3y ⇒ y = -2/3x

By substitution find the points:

(0, 0) and (-1.385, 0.923)

Find midpoint between these two points:

x = (0- 1.385)/2 = -0.6925 , y = (0 + 0.923)/2 = 0.4615

Find perpendicular bisector passing through this point:

y - 0.4615 = 3/2(x + 0.6925)y = 1.5x +  0.4615 + 1.5(0.6925)y = 1.5x + 1.50025

Find intersection of the lines, it is the center:

y = 1.5x + 1.50025x + 2y + 8 = 0

Solving we get:

x = -2,75, y = -2.625

Find radius, the distance from center to point (0, 0) and get equation of circle:

(x + 2.75)² + (y + 2.625)² = (0 + 2.75)² + (0 + 2.625)²x² + 5.5x + y² + 5.25y = 04x² + 22x + y² + 21y = 04x² + 4y² + 22x + 21y = 0

Answer:

Answer is in the picture

write the equation in slope intercept form for the line that passes through the point (1,2) and has a slope of -5

Answers

Answer:

y = -5 × 1 + 2

Step-by-step explanation:

y = y, m = slope, x = x point given (1), b = y point given, unless a zero (2)Formula - y = mx + bPlug it iny = -5 × 1 + 2

Which statements are true? Select three options

Answers

Answer:

Your not showing the picture

Step-by-step explanation:

Answer:

yes but the picture is not shown here

A rectangle has a width of 9 units and a length of 40 units. What is the length of a diagonal?

31 units
39 units
41 units
49 units

Answers

Answer: 41 units


Step 1: Write sample equation

This type of problem can be solved using Pythagorean theorem. In case you are unfamiliar with this type of formula, it is helpful to write the sample equation as the first step. Let’s put this below.

a²+b²= c²

The a and b will stand for the legs, in this case the width and the length. The c will be the diagonal, also referred to as the hypotenuse.

Step 2: Substitute numbers

Now that we have the information on the equation format, let’s substitute the numbers accordingly.

a²+b²= c²
9²+40²= c²

Since we are solving for the hypotenuse, the third value will remain as c.

Step 3: Solve

For the final step, let’s solve for c.

*Rewrite equation*
9²+40²= c²
*Find the squared value of each number*
81+1,600= c²
*Add 81 and 1,600*
1,681= c²
*Cancel out the squared sign by finding the square root of 1,681 and c²*
41= c²

This is your answer! The diagonal is equal to 41. Hope this helps! Comment below for more questions.

Answer:

C or 41 units

Step-by-step explanation:

Just took the test !

i need help asap i will give brianlist

Answers

Answer:

the answer to this is a negative association.

the answer to this is what the other person said

Which product is greater than 3/4?

Answers

Answer:

4/4

Step-by-step explanation:

5/4 and so on with other numer that is higher than 3/4 lol

como convertir una fraccion en numero entero

Answers

Answer:

Para convertir una fracción (n/m) a un número entero tenemos que dividir el numerador entre el denominador. Es decir, el número que se encuentra expresado como n (parte superior) entre el número expresado como m (parte inferir).

Step-by-step explanation:

Answer:

Para convertir una fracción en un número entero: Divida el numerador por el denominador, solo si el numerador es un múltiplo del denominador. Veamos un ejemplo de esta conversión.

Step-by-step explanation:

tenemos 4/2

Dado que 4 es un múltiplo de 2, podemos escribir 4/2 = 2

Espero que esto ayude!

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