Suppose that the test score of a student taking the final of a probability course is a random variable with mean 76.

Required:
a. Give an upper bound for the probability that a student's test score will exceed 86. Suppose, in addition, that the professor knows that the variance of a student’s test score is equal to 25.
(b) What can be said about the probability that a student will score between 65 and 85?
c. How many students would have to take the examination to ensure, with probability at least .9, that the class average would be within 5 of 75? Do not use the central limit theorem.

Answers

Answer 1

Answer:

a. 0.8837

b. 0.6914

c. 10 student

Step-by-step explanation:

a. using markov's inequality; P(u >= X)<= E(u) / X

   mean u = 76

   X, test score = 86

= 76 / 86 = 0.8837

b. variance v = 25

   The test is between 65 and 85 P(65 <= X <= 85);

   P(|65 - X|<= |X - u| <= |85 - X|) = P(65 - 76 <= |X - u| <= 85 -76)

   = P(-11 <= |X - u| <= 9)

   = P(|X - u| <= 9)

using the chebyshev's inequality;

P(|X - u| <= 9) = 1 - variance / (standard deviation of individual test score)^2

   = 1 - 25/ 9^2

   = 1 - 25/81 = 1 - 0.3086 = 0.6914

c. P(|X - 76| <= 5) = 0.9

still using chebyshev's inequality;

= 1 - variance / lower limit^2 (E)

where E = 1 - 0.9 = 0.1

lower limit = 5

= 1 - 25/ 5^2 (0.1) = 10


Related Questions

Prove that: 6^7-6^6+6^5 is divisible by 31
15 points!!!

Answers

Step-by-step explanation:

[tex]6^7-6^6+6^5=6^{5+2}-6^{5+1}+6^5\\\\\text{use}\ a^n\cdot a^m=a^{n+m}\\\\=6^5\cdot6^2-6^5\cdot6^1+6^5\\\\\text{use the distributive property}\ a(b+c)=ab+ac\\\\=6^5\cdot(6^2-6^1+1)=6^5\cdot(36-6+1)=6^5\cdot31\\\\6^7-6^6+6^5=6^5\cdot31[/tex]

therefore it's divisible by 31

[tex](6^7-6^6+6^5):31=(6^5\cdot31):31=6^5[/tex]

[tex]6^7 - 6^6 + 6^5[/tex] is divisible by 31.

What is an expression?

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

[tex]6^7 - 6^6 + 6^5[/tex] s

Taking common factors.

[tex]6^5[/tex] (6² - 6 + 1)

[tex]6^5[/tex] (36 - 6 + 1)

[tex]6^5[/tex] x 31

This is divisible by 31.

Thus,

[tex]6^7 - 6^6 + 6^5[/tex] is divisible by 31.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ2

Suppose we have universal set U. What does it mean to say that X is a subset of U?

Answers

Answer:

All of the elements of X are elements of U.

Step-by-step explanation:

Which number line best represents the solutions to 7 < -2x + 3?

Answers

Answer:

B or D

Step-by-step explanation:

OK ILL SAY IT PEOPLE WANT MONEY TO ANSWER PROBLEMS HERE If the mean of six nu m b e rs is 48, does one
of the nu m b e rs have to be 48? Explain
why or why not. Give an example with six
nu m b e rs to show your answe

Answers

Yes, one of the numbers has to be 48 because the mean of numbers is all the numbers added together, and then divided by how many numbers you added. In this case, we have the mean of 6 number is 48. Now if you think about it,
48*6 = 288
And if you divide 288 by 6, you get:
288/6 = 48.
To make it easier for you to understand, let’s do the original way of finding the mean of this, so :
48 + 48 + 48 + 48 + 48 + 48 = 288
There are six 48’s right? So we divide :

48+48+48+48+48+48
——————————— = 48.
6

11
Resel
A line passes through the points (2, 2) and (-4,-2). What is the equation in standard form of
the line?
A 2x - 3y = -2
B 2x - 3y = 2
C 2x + 3y = -2
D 2x + 3y = 2

Answers

C because the slope is 3/2 with y at -2

I NEED HELP ASAP PLS

Answers

Answer:

2/3

Step-by-step explanation:

to move from one point to another (from left to right) you move up two and to the right 3

Answer:

The slope is 2/3

Step-by-step explanation:

The line goes up 2 points and to the right 3 points so if you do rise/run you get 2/3 as the slope.

HELPPPPPP MEEEE!! A deep-sea diver found an amazing reef 15 kilometers below sea level. What integer would represent this situation

Answers

Answer:

-15

Step-by-step explanation:

Sea-level can be seen as 0 on a number line. The Diver is going below the sea-level, so think of this as him going below the number zero, into the negatives. He is going down 15km, so -15km would represent the integer (whole number) that you're looking for.

this app is bad its s lie​

Answers

IKR like I need answer and it takes so long to someone answer:”c but sometimes it helpful

I need help please!:D

Answers

Answer:

176 R. 5

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

176r5 first

The two parallelograms below are similar.

What is the length in inches of line PQ?

A. 38 in
B. 34 in
C. 40 in
D. 14 inch

Answers

PQ = 40 inches
The answer is C

Sam is reading a book. He finishes 6 pages of the book in 18 minutes. How many pages would Sam have finished reading in 36 minutes?

Answers

Answer:

12 pages

Step-by-step explanation:

This is a fairly straight forward question.

Sam read 6 pages in 18 minutes, and we want to know how many pages he could have finished if he read for 36 minutes.

36 minutes is double the time of 18 minutes.

So we just have to double the 6 pages Sam read into 12 pages and that is the answer.

can u pls help me with this question ​

Answers

D. because 9:45 and 12:60 because if you divide y by x it’s 5, while 3:12 and 6:24 are 4

what is the coordinates of the point where y-4x=1 crosses the y-axis​

Answers

Answer:

(0, 1)

Step-by-step explanation:

you have to put the equation in the slope point form

y=mx+b and here b is the y-intercept (where it crosses the y axis)

y-4x=1 add 4x to both sides

y=4x+1 so the coordinats are (x=0, y=1)

A sea lion was swimming at 2 feet below sea level. The number line shows
the location of the sea lion. It then swam down 8 feet. Describe how to use
the number line to find the new location of the sea lion.
109 8-7 654 3 -2-1 0 1 2 345 6789 10
OA. On the number line, move 8 units to the right. End at 10. The sea
lion was 10 feet above sea level.
OB. On the number line, move 8 units to the left. End at -6. The sea
lion was 6 feet below sea level.
O C. On the number line, move 8 units to the left. End at -10. The sea
lion was 10 feet below sea level.
OD. On the number line, move 8 units to the right. End at 6. The sea
lion was6 feet above sea level.
EPREVIOUS

Answers

Answer:

C. On the number line, move 8 units to the left. End at -10. The sea

lion was 10 feet below sea level.

Step-by-step explanation:

hope I helped

Help please stat! Brainlist!

Answers

Answer:  11.71 meters per second.

PLZ CORRECT ME IF I AM WRONG thxs and have a lovely day :)

Step-by-step explanation:

Gabriel earned $238.40 at His job when he word for 16 hours what was his hourly wage in dollars per hour?

Answers

Answer:

$14.9

Step-by-step explanation:

238.40 / 16 = $14.9 hourly

Answer:

Gabriel earns $14.90 per hour

Step-by-step explanation:

238.4 divided by 16 gives you 14.9

Hope this helps

please can someone help me!! :(

Answers

Answer:

G

Step-by-step explanation:

Distribute the -7 to 4x and -5

Answer:

Hey!

The answer is

-7x (4x - 5)

When you multiply them you get

[tex]-28x^{2} + 35[/tex]

So, Option G is the right answer!

Amy has an adjusted gross income of $85,600. For the house she is considering buying, her monthly mortgage payment would be $1,711.22, her semi-annual property tax bill would be $3,239, and her annual homeowner’s insurance bill would be $980. She has a credit card bill that averages $500 per month and a $475 car payment. What is her back-end ratio?​

Answers

Answer:

85,600:6,905.22

Step-by-step explanation:

When multiplying, the answer is negative when you:

A: multiply a positive (+) times a negative (-)

B: multiply a negative (-) times a negative (-)

C: multiply a positive (+) times a positive (+)

Answers

Step-by-step explanation:

b: multiplying a negative (-) by a negative (-)

HOw do I complete all my homework on time? I have a BUNCH of homework

Answers

Answer:

One helpful technique I used to stay focused is to buy a pack of m&ms or mini  candies and every time I complete a problem I eat one candy or m&m. Also, try making a goal for yourself for example "my goal is to complete 100 problems in an hour"

Step-by-step explanation:

I hope this helps

message me with any more questions u have

I need help.........​

Answers

Answer:

number 1

Step-by-step explanation:

The answer is number 1

Solve formula as indicated. - F = m + 2a for a

Answers

Answer:

The value of 'a' will be:

[tex]a\:=\:-\frac{f}{2}+-\frac{1}{2}m[/tex]

Step-by-step explanation:

Given the formula

[tex]-F = m+2a[/tex]

Let us solve the equation for 'a'

[tex]-F = m+2a[/tex]

Flip the equation

[tex]2a+m=-f[/tex]

Add -m to both sides

[tex]2a+m+(-m)=-f+(-m)[/tex]

[tex]2a = -f - m[/tex]

Divide both sides by 2

[tex]\frac{2a}{2}=\:\:\frac{-f\:-\:m}{2}[/tex]

[tex]a\:=\:-\frac{f}{2}+-\frac{1}{2}m[/tex]

Therefore, the value of 'a' will be:

[tex]a\:=\:-\frac{f}{2}+-\frac{1}{2}m[/tex]

In how many zeros does 75! end?

Answers

They have 18 zeros this is not

Ellen collected 88 empty cans to recycle,and Carl collected 72 cans. They packed an equal number of cans into each of two boxes to the recycling center

Answers

ellen had 44 per box and carl had 36 per box

but if they had only two boxes altogether then each box had 80 cans in it

The area under the density curve that lies to the right of 11 is 0.322. What percentage of all possible observations of the variable are at most 11?

Answers

Answer: 67.8%

Step-by-step explanation:

The variables that are at most 11 will lie on the left of 11.

The percentage of the possible observations to the left will be:

= 1 - percentage to the right

= 1 - 0.322

= 0.678

= 67.8%

Could someone help me, 1-14 just need 1-14 answers.

Answers

11) 420 in
12) 108 ft
13) 60 ft
14) 75 ft

there are 12 inches in a foot, 3 feet in a yard


Need help please I would really appreciate it

Answers

Answer:

The slope of line is 9

Step-by-step explanation:

We can use two pairs of input-output from the table to find the slope of the given line. Here x is input and y is output.

Slope is defined as the steepness of a line and is given by the formula:

[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]

Selected pairs from table are:

(-1,-18) and (0,-9)

Here

[tex]x_1 = -1\\x_2 = 0\\y_1 = -18\\y_2 = -9[/tex]

Putting the values in the formula

[tex]m = \frac{-9-(-18)}{0-(-1)}\\=\frac{-9+18}{0+1}\\= 9[/tex]

Hence,

The slope of line is 9

Find the value of x.
71°
(10x + 6)°
(13x - 2)°
(8x - 1)
#15

Answers

Answer:

7x7/6x4

Step-by-step explanation:

what is the final position of (-7) + (-2) on a number line ?

Answers

Answer:

answer is A, source: a calculator

Step-by-step explanation:

if you are adding two negitives, take the signs away and add normal, then add the sign back at the end, ONLY WORKS WITH TWO NEGITIVES AND HAS TO BE ADDITION

Answer:

Step-by-step explanation:

It’s 9 because you make 7 and 2 a positive number

I need help with mathematics and I have to ask a couple questions about it​

Answers

so please ask question

Answer:

Sure. What are the questions?

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