The distribution of passenger vehicle speeds traveling on a certain freeway in California is nearly normal with a mean of 71.5 miles/hour and a standard deviation of 4.75 miles/hour. The speed limit on this stretch of the freeway is 70 miles/hour. (a) A highway patrol officer is hidden on the side of the freeway. What is the probability that 5 cars pass and none are speeding? Assume that the speeds of the cars are independent of each other. (Round your answer to four decimal places.) .0074 (b) On average, how many cars would the highway patrol officer expect to watch until the first car that is speeding? (Round your answer to two decimal places.) What is the standard deviation of the number of cars he would expect to watch? (Round your answer to two decimal places.)
Answer:
a
[tex]G = 0.007523 [/tex]
b
The number of cars the highway patrol officer would watch before a car that is seen is [tex]E(X) = 1.6027 [/tex]
The standard deviation is [tex]s = 0.9829 [/tex]
gg
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = 71.5 \ miles/hour[/tex]
The standard deviation is [tex]\sigma = 4.75 \ miles/hour[/tex]
The speed limit is [tex] x = 70 \ miles /hour[/tex]
Generally the probability of getting a car that is moving with speed greater than the speed limit is mathematically represented as
[tex]p =P(X > x ) = P(X > 70) = P(\frac{X - \mu }{\sigma } > \frac{70 - 71.5 }{4.75})[/tex]
=> [tex] p= P(X > 70) = P(\frac{X - \mu }{\sigma } > \frac{70 - 71.5 }{4.75})[/tex]
=> [tex] p= P(X > 70) = P(\frac{X - \mu }{\sigma } > -0.31579 )[/tex]
Here
[tex]\frac{X - \mu }{\sigma } = Z(The \ standardized \ value \ of X )[/tex]
So
=> [tex] p= P(X > 70) = P(Z > -0.31579 )[/tex]
From the z-table
[tex]p = P(Z > -0.31579 ) = 0.62392[/tex]
So
[tex] p = P(X > 70) = 0.62392 [/tex]
Generally the probability of getting a car that is not moving with speed greater than the speed limit is mathematically represented as
[tex]q = 1 - p[/tex]
=> [tex]q = 1 - 0.62392 [/tex]
=> [tex]q = 0.37608 [/tex]
Generally the probability of getting 5 cars that are not speeding is mathematically represented as
[tex]G = q^5[/tex]
=> [tex]G = (0.37608)^5[/tex]
=> [tex]G = 0.007523 [/tex]
Generally the number of cars that the highway patrol officer is expected to watch until the first car that is speeding is gotten is mathematically represented as
[tex]E(X) = \frac{1}{p}[/tex]
=> [tex]E(X) = \frac{1}{0.62392}[/tex]
=> [tex]E(X) = 1.6027 [/tex]
Generally the standard deviation is mathematically represented as
[tex]s = \sqrt{\frac{1 - p }{ p^2} }[/tex]
=> [tex]s = \sqrt{\frac{1 -0.62392 }{ (0.62392)^2} }[/tex]
=> [tex]s = 0.9829 [/tex]
The probability that 5 cars pass and none are speeding is 0.007523 and the number of cars the highway patrol officer would watch before a car that is seen is E(X) = 1.6027
What is normal a distribution?It is also called the Gaussian Distribution. It is the most important continuous probability distribution. The curve looks like a bell, so it is also called a bell curve.
The z-score is a numerical measurement used in statistics of the value's relationship to the mean of a group of values, measured in terms of standards from the mean.
The distribution of passenger vehicle speeds traveling on a certain freeway in California is nearly normal with a mean of 71.5 miles/hour and a standard deviation of 4.75 miles/hour.
The speed limit on this stretch of the freeway is 70 miles/hour.
Generally, the probability of getting a car that is moving with speed greater than the speed limit is mathematically represented as;
[tex]p = P(X > x) = P(X > 70) = P(z = \dfrac{X - \mu}{\sigma } > \dfrac{70 - 71.5}{4.75})\\\\p = P(X > 70 ) = P(\dfrac{X -\mu}{\sigma} > -0.31579)[/tex]
From the z-table
[tex]p = P(X > 70)= P(z > -0.31579) \\\\p = 0.62392[/tex]
Generally, the probability of getting a car that is not moving with speed greater than the speed limit will be
q = 1 - p
q = 1 - 0.62392
q = 0.37608
Generally, the probability of getting cars that are not speeding will be
G = q⁵
G = 0.37608⁵
G = 0.007523
The number of cars that the highway patrol officer is expected to watch until the first car that is speeding is gotten will be
[tex]\rm E(X) = \dfrac{1}{p}\\\\E(X) = \dfrac{1}{0.62392}\\\\E(X) = 1.6027[/tex]
The standard deviation will be
[tex]\sigma = \sqrt{\dfrac{1-p}{p}}\\\\\\\sigma = \sqrt{\dfrac{1-0.63292}{0.62392}}\\\\\\\sigma = 0.9829[/tex]
More about the normal distribution link is given below.
https://brainly.com/question/12421652
Dexter got a raise in his hourly pay, from $12.75 to $16.30. Find the percent change. Round to the nearest tenth of a percent.
Answer:
27.8
Step-by-step explanation:
16.3 - 12.75 = 3.55
3.55 ÷ 12.75 = 27.8
What is the 50th term for -7,-2,3 ...?
a(50) = 238
Step-by-step explanation:The constant (diference) = 5
-2 - (-7) = - 2 + 7 = 5
3 - (-2) = 3 + 2 = 5
use formula
a(n) = a + (n - 1)d
a = - 7
n = 50
d = 5
a(50) = - 7 + (50 - 1)5
= - 7 + 49ₓ5
= - 7 + 245
= 238
Good luck !
How could you informally prove to your friend that you have been working with a trainer at the gym.
You can show your gym bill.
You can show your membership card.
You can demonstrate some of the exercises that your trainer taught you.
You can show your before and after charts for your muscle mass.
Answer:
You can demonstrate some of the exercises that your trainer taught you
Step-by-step explanation:
The rest of the options are too formal.
You can demonstrate some of the exercises that your trainer taught you. The correct option is C.
what is convincing communication?Persuasive communications include a variety of attributes designed to increase persuasions, such as an appealing source, a message with convincing arguments, or efforts to make the topic seem personally relevant to the audience.
You can prove to your friend that you have been working with a trainer at the gym by demonstrating some of the exercises that your trainer taught you.
Therefore, you can demonstrate some of the exercises taught to you by your trainer. C is the correct answer.
To know more about convincing communication follow
https://brainly.com/question/25793182
#SPJ2
Write an equation of the line passing through each of the following pairs of points. c (4, 0), (−2, 8)'
Answer:
Step-by-step explanation:
First, you must find the slope of the line using the formula (y2-y1/x2-x1). For your problem that would be (8-0/-2-4)= -4/3.
Then, you would plug in the slope and the y-intercept into the slope-intercept formula (y=mx+b), where m is the slope and b is the y intercept (4).
Your answer would be y=-4/3x+4
Which of the following is not true?
[tex]4\pi > 12[/tex]
[tex]\sqrt{18 } + 2 < \frac{15}{2} [/tex]
[tex]6 - \sqrt{35} < 0[/tex]
[tex] \sqrt{16} + 4 > \sqrt{4} + 5[/tex]
Answer: 6 - √35 < 0
----------------------------
el perímetro de un cuadrado es de 24 ft ¿cuál es la longitud de los lados?
Answer:
English?
Step-by-step explanation:
what is the sum of 1/3+3/6=
Answer:
5/6
Step-by-step explanation:
³√3000- ³√375 simplify
Answer:
30√30 - 15√15
Step-by-step explanation:
I'm not 100% sure
Answer:
We can write³√3000- ³√375 as [tex]\sqrt[3]{5*5*5*2*11}-\sqrt[3]{5*5*5*3}[/tex]
[tex]\sqrt[3]{5*5*5*2*11}-\sqrt[3]{5*5*5*3}[/tex]= [tex]5\sqrt[3]{22} -5\sqrt[3]{3}[/tex]
[tex]5\sqrt[3]{22} -5\sqrt[3]{3}[/tex] is the simplest form of ³√3000- ³√375
PLZ HELP FAST!!!!!!!!
Answer:
-6, -1, 4, -1
Step-by-step explanation:
If you plug it in thats what you get
The column headers of a formal proof are _____________ and ____________.
statements and reasons
definitions and examples
givens and conclusions
conjectures and counterexamples
Answer:
Statements and reasons
Step-by-step explanation:
Answer:
statements and reasons
Step-by-step explanation:
These headers are standard and are used on every formal proof.
37 degree 79 degree what is the value of n
Answer:
64
Step-by-step explanation:
The angles all add up to 180. 37 plus 79 is 116. 180-116=64.
Hope this helped! If it did, please let me know by marking it the brainliest!
In a week, 12 hens laid 84 eggs. What is the unit rate for eggs per hen?
Answer:
7 eggs per hen
Step-by-step explanation:
There were 84 eggs laid between the 12 hens. That means the 84 eggs are split among the 12 hens. 84 divided by 12 = 7.
Please help!! ASAP!! Graph Y=3/8x-2
Every week I buy four 2-litre bottles of lemonade whilst shopping at my local supermarket. Last week the bottles on the shelf were limited edition “2.5 litres for the price of 2 litres” bottles, and the supermarket also had a “buy 3 bottles, get another one free” offer.
In terms of cost per litre, by what percentage was the cost of my four bottles of lemonade lower than usual last week?
Answer:
40%
Step-by-step explanation:
Every week you he buys 4 number of 2 Litres bottle of lemonade.
Thus, let's say cost of each bottle is X.
This means he total cost is 4X
Now, total litres = 4 × 2 = 8 litres
Thus, cost per litre = 4X/8 = ½X
Now, we are told that Last week the bottles on the shelf were limited edition “2.5 litres for the price of 2 litres” bottles ".
This means that now, it is cheaper.
However, the supermarket also had a “buy 3 bottles, get another one free” offer.
Now since he buys 8 litres weekly, now since it's 2.5 L bottle, he will buy 3 since he will be given 1 free for every 3 he buys.
Thus, total litres he is paying for = 2.5 × 3 = 7.5 litres
Thus, cost per bottle is; 3X
Since he is getting 1 bottle free, then total bottle he gets is; 7.5 L + 2.5 L = 10L
Thus;
cost per litre is now; 3X/10
Difference in costs per litre is;
½X - 3X/10 = X/5
percentage of the cost of four bottles of lemonade lower than usual last week = (X/5)/(½X) × 100% = 2/5 × 100% = 40%
On average, Joanne writes
9 emails per day. How long
will it take Joanne to write
279 emails?
Answer:
It will take 31 days (4 weeks and 3 days) to write 279 emails
Step-by-step explanation:
279 emails ÷ 9 emails per day = 31 total days to write 279 emails
Geometry sucks I need help im really behind
Answer:
26°
Step-by-step explanation:
[tex]m\angle WXZ = 78\degree... (given) \\\\
m\angle 2 = 2m\angle 1...(given)... (1)\\\\
\because m\angle 1 + m\angle 2=m\angle WXZ \\\\
\therefore m\angle 1 + m\angle 2=78\degree... (2)\\\\
\therefore m\angle 1 + 2m\angle 1=78\degree\\ [From\:equations\: (1)\: \&\:(2)] \\\\
\therefore 3m\angle 1=78\degree\\\\
\therefore m\angle 1=\frac{78\degree}{3}\\\\
\therefore m\angle 1=26\degree \\[/tex]
Please help, explain and correct the mistake on the picture below, marking brainliest!
Answer:
see below
Step-by-step explanation:
2/3 x = -6
Multiply each side by the reciprocal to isolate x
3/2 * 2/3x = -6 * 3/2
x = -9
The number of milligrams of a certain medicine a veterinarian gives to a dog varies directly with the weight of the dog.
If the veterinarian gives a 30-pound dog 5 milligram of the medicine, which equation relates the weight, w, and the
dosage, o?
Question: The number of milligrams of a certain medicine a veterinarian gives to a dog varies directly with the weight of the dog. If the veterinarian gives a 30-pound dog 3/5 milligram of the medicine, which equation relates the weight,w, and the dosage, d?
Answer: d= 1/50w
Explanation: I took the test in Edgenuity.
Hope this helps!
what is 46.025 written in scientific notation?
Each square in the periodic table contains the element's atomic number, chemical symbol, name, and atomic mass.
True or false?
Answer:
True...
Step-by-step explanation:
Answer:
true
Step-by-step explanation:
Please I need help 20 POINTS!
The question States: come up with a story problem that matches the above representations. (There all apart of the same problem)
HELP PLS 100PTS!!!
Evaluate s(-19)
s(n)=7-4n
Answer: Therefore, the recursive formular is A(n) = A(n - 1) + 9
Step-by-step explanation: (n) = 2 + 9(n - 1) = 2 + 9n - 9
(n + 1) = 2 + 9(n + 1 - 1) = 2 + 9n = (2 + 9n - 9) + 9 = A(n) + 9
What is five to the second power in expanded form and standard
Step-by-step explanation:
Answer:
5x5 and 5^2
Step-by-step explanation:
hope this helps.
A jet and a light plane leave the same airport at the same time and travel in opposite directions at 960 km/h and 560 km/h, respectively. In how many hours will they be 4560 km apart?
The jet travels a distance of
(960 km/h) t
after time t, while the light plane travels a distance of
(560 km/h) t
The jet is faster than the light plane, so the distance between them is
(960 km/h) t - (560 km/h) t = (400 km/h) t
so the time it takes for them to be 4560 km apart is
(400 km/h) t = 4560 km
==> t = (4560 km) / (400 km/h)
==> t = 11.4 h
18x-(3x+9) expression and equations
Answer:
15x−9
Step-by-step explanation:
Speedie ran the 200 meter race in 25.5 seconds. How much of an hour did it take Speedie to run
the race? 1.0 hour = 3600.0 seconds
Answer:
Speedie ran the race in 0.708(3)% of an hour, the 3 in the parentheses means the 3 repeats forever
Step-by-step explanation:
We have 25.5/3600, and when we convert it to a decimal, we have 0.00708(3), the 3 in the parentheses means the 3 repeats forever. To convert it to percentage, we multiply it by 100, to get 0.708(3). Hope it helps!
Calories consumed by members of a track team the day before a race are normally distributed, with a mean of 1,600 calories and a standard deviation of 100 calories. If a normal curve is sketched using these data, what is the range for 3 standard deviations to the right and to the left of the mean?
Answer:
600 calories
Step-by-step explanation:
John has consumed 1600 calories out of which he has burned off 400. So the total calories for the day so far are:
1600-400
=1200 calories
He has to keep the count of calories upto 1800 per day and the consumed calories so far are 1200
So he needs to burn:
= 1800 - 1200
= 600 calories
He has to consume 600 calories more..
Hence 1000 is not a viable solution to the problem as the remaining count of calories that need to be consumed are 600 ..
Answer:
The Answer is A.
Step-by-step explanation:
Hope this helps!
HELPPP PLEASE!!!! SHOW ALL WORK!!!
Answer:
x=54
Step-by-step explanation:
these two angles are supplementary to each other. this is because alternate interior angles are congruent, and 2x+42 degrees is supplementary to the alternate interior angle of x-24 degrees. so, we can add these two numbers up and set it equal to 180.
2x+42+x-24=180
3x+18=180
3x=162
x=54
if this question is asking for x, 54 is the answer. if it is asking for the angle measures, plug in 54 for x for each angle and solve.
Which binomial is a factor of the following quadratic? K2-12k+36
9514 1404 393
Answer:
(k -6)
Step-by-step explanation:
The given quadratic is a perfect square, so has one repeated binomial factor:
k^2 -12k +36 = (k -6)^2