Assume that the random variable X is normally distributed, with mean and standard deviation . Compute the probability. Be sure to draw a normal curve with the area corresponding to the probability shaded.
Answers
Using the normal distribution, the probability that x is of at most 40, represented by option B, is given as follows:
[tex]P(X \leq 40) = 0.1587[/tex]
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation of the distribution are given, respectively, by:
[tex]\mu = 51, \sigma = 11[/tex]
The probability that x is of at most 40 is the p-value of Z when X = 40, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{40 - 51}{11}[/tex]
Z = -1
Z = -1 has a p-value of 0.1587.
Hence the probability is:
[tex]P(X \leq 40) = 0.1587[/tex]
Which is the part to the left of X = 40 of the distribution, hence option B is correct.
More can be learned about the normal distribution at https://brainly.com/question/28135235
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Related Questions
A road is 3/5
of a mile long. A crew needs to repave 3/7
of the road. How long is the section that needs to be repaved?
Write your answer is simplest form.
Answers
Answer:
9/35
Step-by-step explanation:
3/5 x 3/7
Gracie went for a morning walk and met her old friend Suzie and her daughter Jennie after a long time. Gracie asked Suzie how old is Jennie to which Jennie replied “In two years I will be twice as old as I was three years ago”. How old is Jennie?
Answers
Solve the given differential equation by using an appropriate substitution. The DE is a Bernoulli equation. t2 (dy/dt) + y2 = ty
Answers
Answer:
Step-by-step explanation:
[tex]t^2 \dfrac{dy}{dt}+ y^2 = ty \\ \\ t^2 \dfrac{dy}{dt}-ty = -y^2[/tex]
[tex]\text{by dividing both sides by }{y^2},\text{ we have:}[/tex]
[tex]\dfrac{t^2}{y^2}\dfrac{dy}{dt}- \dfrac{ty}{y^2}= -1[/tex]
[tex]\dfrac{t^2}{y^2}\dfrac{dy}{dt}- t\dfrac{1}{y}= -1[/tex]
[tex]\text{by dividing both sides by }t^2; \text{we have;}[/tex]
[tex]\dfrac{1}{y^2}\dfrac{dy}{dt}- \dfrac{1}{t}\dfrac{1}{y}= -\dfrac{1}{t^2}--- (i)[/tex]
[tex]Let \ v = \dfrac{1}{y}[/tex]
[tex]\dfrac{dv}{dt}= -\dfrac{1}{y^2}\dfrac{dy}{dt}[/tex]
[tex]-\dfrac{dv}{dt}= \dfrac{1}{y^2}\dfrac{dy}{dt}[/tex]
[tex]\text{replace in equation (1); we have}[/tex]
[tex]- \dfrac{dv}{dt}-\dfrac{1}{t}v = -\dfrac{1}{t^2}[/tex]
[tex]- \Big ( \dfrac{dv}{dt}+ \dfrac{1}{t}v \Big) = -\dfrac{1}{t^2}[/tex]
[tex]\dfrac{dv}{dt}+\dfrac{1}{t}v = \dfrac{1}{t^2}[/tex]
[tex]\text{relating above with} \dfrac{dv}{dt}+ P(t) v = Q(t) \text{, we have:}[/tex]
[tex]P(t) = \dfrac{1}{t} \ \ \ , \ \ \ \ Q(t) = \dfrac{1}{t^2}[/tex]
[tex]\mu (t) = e^{\int P(t) \ dt }= e ^{\int \dfrac{1}{t} \ dt}= e^{In|t|}= t[/tex]
[tex]v\mu(t) = \int \mu(t) Q(t) dt + C[/tex]
[tex]vt = \int (t) (\dfrac{1}{t^2})dt + C[/tex]
[tex]vt = \int \dfrac{1}{t}dt + C[/tex]
[tex]vt = Int+C[/tex]
[tex]v = \dfrac{In \ t + C}{t}[/tex]
[tex]\text{substitute } v = \dfrac{1}{y}}, we \ get}[/tex]
[tex]\dfrac{1}{y}=\dfrac{In \ t +C}{t}[/tex]
[tex]\mathbf{y = \dfrac{t}{In \ t + C}}[/tex]
Cuanto es la rais cuadrada del rectángulo entre dos y multiplicada por 1837
Answers
14,696
buen dia
(lo siento)
If the probability of an event is
and there are 28 total outcomes, how many favorable outcomes are there?
0 1
04
07
O 28
PLEASE ANSWER AND HURRRRRRY
Answers
Answer:
uhhh 28
Step-by-step explanation:
HELP ASAP PLS SHOW WORK
Answers
Answer:
42
dnndndndndndnd
dndndndndj
Write an expression to represent “7 less than 6 times a number n.”
Answers
Answer:
7 < 6n
Step-by-step explanation:
Answer:
6n-7
Step-by-step explanation:
7 Less = -7
6 x n = 6n
Combine an expression we get 6n - 7
Can someone help me with a two step equatio that is x=2
Answers
Help!! Find the area of the triangle.
Answers
Answer:
Area = 60.0 units²
Step-by-step explanation:
First, let's find the height of the triangle using Pythagorean Theorem:
Height = √(11² - 8²)
= √57
Height = 7.5 (nearest tenth)
✔️Find the area:
Area = ½*base*height
Base = 2*8 = 16
Height = 7.5
Plug in the values
Area = ½*16*7.5
Area = 60.0 units² (nearest tenth)
need help with this tricky question. thanks
Answers
Answer:
E
Step-by-step explanation:
GF is 6 so GE is 3
this is one of the pythagorean triples
which is 3,4,5
since there is already 3 and 5, length HE is 4
Hace 9 meses que no llueve cual es el número entero
Answers
hnAnswer:
gjunn
Step-by-step explanation:
Answer:
en un menos de 9 meses
ya que es desmunusion es de 0
What is the slope of y = -x + 7?
Answers
Answer:
The slope is -1
[tex]53 \times \frac{8}{6} [/tex]
i dont know how to do it can u show me
Answers
Answer:
What do you want your answer in? Exact or decimal form?
Exact form: 212/3
Decimal form 70.6
Step-by-step explanation:
Cancel the common factor of 8 and 6 for 53 * 4/3. Multiply 53(4/3), 212/3. This would be the answer for the exact form, decimal form is created by dividing 212 by 3, for 70.66666--.
____
1x6
Do that and ur answer
hello help me please
Answers
Answer:
Step-by-step explanation:
divide each by 2 and see if you can get a proper fraction
Consider the first four terms of the sequence below.
1, -1/2, 1/4, -1/8, ...
What is the 8th term of this sequence?
A. -1/256
B. 1/128
C. -1/128
D. 1/256
Answers
Answer:
the answer is C.-1/128......
choose the right multiplacation equation that is correct A.16x6=22 B.16x6=636 C.16x6=96 D.16x6=123
Answers
Answer:
C. 16 · 6 = 96
Step-by-step explanation:
16 · 6 = 96, therefore option C is the correct choice :)
Answer:
The right multiplication equation that is correct is (C.16×6=96)
If x=9 in what is the surface area of the geometric shape formed by this net?
Answers
Answer:
1134 in²Step-by-step explanation:
Surface area is:
x²*2 + 3x*x*4 = 14x²Substitute x:
14x² = 14*9² = 1134 in²y = 4x - 11
4x - y = 11
Systems of equations by substitution
Answers
Answer:
............................
Answer:
No Solution
Step-by-step explanation:
Substitute y = 4x - 11 in 4x - y = 11
4x - y = 11
4x - 4x - 11 = 11
-11 = 11
There is no solution because -11 does not equal 11.
I need some help please !
Answers
Answer:
With what?
Step-by-step explanation:
Pat finds that the length of a ceiling beam is 114 inches what is the length of the beam in feet.
how to work it out in a problem
Answers
Answer:
farted farted fartedfarted
Answer
Step-by-step explanation:
The legend on a map states that 1 inch
is 250 miles. If you measure 3 inches
on the map, how many miles would
the actual distance be?
Answers
In this rectangle the base is 1 cm more than the hight
Answers
Answer:
the equation is base = height + 1
No it's not is 67 and 23
Answers
Answer:
What?
Step-by-step explanation:
I don't understand.
Solve for t.
45 = 5t + 45
Answer:
Submit Answer
Answers
Answer:
0
Step-by-step explanation:
45=5t+45
-45=-45
0=5t
/5
0=t
Hope this helped :)
Answer:
T=0
Step-by-step explanation:
Subtract 45 from both sides and then simplify then divide bith sides of the equation by the same term
An elementary school class ran 1 mile in an average of 11 minutes with a standard deviation of 3 minutes. Rachel, a student in the class, ran 1 mile in 8 minutes. A junior high school class ran 1 mile in an average of 9 minutes, with a standard deviation of 2 minutes. Kenji, a student in the class, ran 1 mile in 8.5 minutes. A high school class ran 1 mile in an average of 7 minutes with a standard deviation of 4 minutes. Nedda, a student in the class, ran 1 mile in 8 minutes.
Required:
a. Why is Kenji considered a better runner than Nedda, even though Nedda ran faster than he?
b. Who is the fastest runner with respect to his or her class? Explain why.
Answers
Answer:
Step-by-step explanation:
a.
Kenji ran faster than the class average by 0.25 of a standard deviation while Nedda was slower than the average in her class.
b.
Rachel: average - 1st deviation
Kenji: average - 0.25 standard deviation
Nedda: slower than average so it's definitely not her.
Since Rachel is faster than the average and differs by the most standard deviations compared with Kenji,
So, Rachel is the faster one.
the coast of 16 pens is rupees 256. Find the cost of 13 pens.
Answers
So, 16x13=208
Answer: 208
Comans Corporation has two production departments, Milling and Customizing. The company uses a job-order costing system and computes a predetermined overhead rate in each production department. The Milling Department's predetermined overhead rate is based on machine-hours and the Customizing Department's predetermined overhead rate is based on direct labor-hours. At the beginning of the current year, the company had made the following estimates:
Milling Customizing
Machine-hours 18,000 13,000
Direct labor-hours 4,000 7,000
Total fixed manufacturing overhead cost $ 113,400 $ 64,400
Variable manufacturing overhead per machine-hour $ 1.60
Variable manufacturing overhead per direct labor-hour $ 3.90
During the current month the company started and finished Job A319. The following data were recorded for this job:
Job A319: Milling Customizing
Machine-hours 60 10
Direct labor-hours 20 60
Direct materials $ 655 $ 305
Direct labor cost $ 400 $ 1,200The amount of overhead applied in the Milling Department to Job A319 is closest to:
A. $552.00
B. $474.00
C. $142,200.00
D. $96.00​
Answers
Answer:
Comans Corporation has two production departments, Milling and Customizing. The company uses a job-order
five and three sixths minus two and one third
Answers
Answer:
19/6
Step-by-step explanation:
5 3/6 - 2 1/3 = 19/6
The factors of x² and x and x - 5.
A. True
B. False
Answers
A.True
True hai
mujhe brainliest mark karde agar nahi kiya toh tujhe report kardunga
Hope this helps :)
The function f is defined by f(x) = x + 3 / 4x - 5 . Find f(x+3).
Answers
Answer:
x+6 / 4x-5
Step-by-step explanation: