1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
MA_775_DIABLO [31]
3 years ago
6

the marks in an examination for a Physics paper have normal distribution with mean μ and variance σ2 . 10% of the students obtai

n more than 75 marks and 20% of them obtained less than 40 marks. find the value of  μ  and σ​
Mathematics
1 answer:
Blababa [14]3 years ago
3 0

Let X be the random variable for the number of marks a given student receives on the exam.

10% of students obtain more than 75 marks, so

P(X>75)=P\left(\dfrac{X-\mu}\sigma>\dfrac{75-\mu}\sigma\right)=P(Z>z_1)=0.10

where Z follows a standard normal distribution. The critical value for an upper-tail probability of 10% is

P(Z>z_1)=1-F_Z(z_1)=0.10\implies z_1=F_Z^{-1}(0.90)

where F_Z(z)=P(Z\le z) denotes the CDF of Z, and F_Z^{-1} denotes the inverse CDF. We have

z_1=F_Z^{-1}(0.90)\approx1.2816

Similarly, because 20% of students obtain less than 40 marks, we have

P(X

so that

P(Z

Then \mu,\sigma are such that

\dfrac{75-\mu}\sigma\approx1.2816\implies75\approx\mu+1.2816\sigma

\dfrac{40-\mu}\sigma\approx-0.8416\implies40\approx\mu-0.8416\sigma

and we find

\mu\approx53.8739,\sigma\approx16.4848

You might be interested in
0.099
ioda
The answer to your question is 0.469
3 0
3 years ago
Of all the species in the world, 4 out of every 5 are insects what percentage of species are insects
Fiesta28 [93]

Answer:

80%

Step-by-step explanation:

So you basically, just make it a ratio. Since a percentage is out of 100, just make the 5 into 100. To get 5 to 100, you times 20. Then you do the same thing to the 4 which you get 80.

5 0
3 years ago
The triangular faces of the peaks on a roof are congruent isosceles triangles with vertex angles U and V.
Rina8888 [55]

Answer:

<em> (a). ∠UXV, ∠XVY ; (b). UV = 8 m .</em>

Step-by-step explanation:

3 0
3 years ago
Reducing Fractions<br> 30/90
fgiga [73]

Answer: 1/3

<u>Divide</u>

30/90÷30/30=1/3

Since we are simplifying fractions we divide the numerator and the denominator by a number the fraction can go into.

We could use 10 then divide by 3. You can also just divide by 30 and get the answer.

Let's try dividing by 10 then 3!

30/90÷10/10=3/9

3/9÷3/3=1/3

As you can see we still get 1/3 when we divide by 3. Even tho you have to divide twice you still get 1/3. That's all that matters.

3 0
3 years ago
Which equation has the same solutions as 2x^2+16x-10=0 a) (x+4)^2=-3 b) (x+4)^2=-11 c) (x+4)^2=13 d) (x+4)^2=21
ikadub [295]
I'm working on the same thing down load the algebra tiger it really helps a lot I promise I use it daily to help with these
4 0
3 years ago
Other questions:
  • If 20 is increased by 50%, what is the new amount?
    11·1 answer
  • -3 5/6 - 4 3/8<br><br>Please help​
    11·1 answer
  • After completing the fraction division 8 divided by 1/6, Patel used the multiplication below to check his work. 1/48 x 6 = 1/48
    15·2 answers
  • A pizza was divide
    14·2 answers
  • ABCD is a parallelogram. If / increases, then / A. remains the same B. doubles C. increases D. decreases
    13·2 answers
  • A study shows that 84​% of the population of all calculus students consider calculus an exciting subject. Suppose 29 students ar
    9·1 answer
  • The driveway needs to be resurfaced. what is the BEST estimate of the area of the driveway?​
    15·1 answer
  • Which of the following goes through (-2,4)
    12·1 answer
  • PLEASE HELP!!!! <br> Geometry
    8·1 answer
  • What is the inverse of this function?<br> f(1)<br> 3<br> r + 12
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!