Answer:
0.98 = 98% probability that the average midterm score of these students is at most 75 points.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The average midterm score of students in a certain course is 70 points.
This means that [tex]\mu = 70[/tex]
29 students are randomly selected and the standard deviation of their scores is found to be 13.15 points.
This means that [tex]\sigma = 13.15, n = 29, s = \frac{13.15}{\sqrt{29}} = 2.44[/tex]
Find the probability that the average midterm score of these students is at most 75 points.
This is the pvalue of Z when X = 75. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{75 - 70}{2.44}[/tex]
[tex]Z = 2.05[/tex]
[tex]Z = 2.05[/tex] has a pvalue of 0.98.
0.98 = 98% probability that the average midterm score of these students is at most 75 points.
15, 19, 23, 27.... what is the 52nd term in the arithmetic sequence?
Answer:
219
Step-by-step explanation:
a is the number needed to add from the first to the second which is 4(must be constant)
b is the term zero means 15-a which is 15-4=11
WHAT'S 675 DIVIDED BY 8 HELPPPP PLEASE TELL ME THE NUMBERS TO SHOW MY WORK
Answer:
85.625 is the answer
Step-by-step explanation:
or, 85 whole 5/675
Simplify:
a) 3x + 5y - x + 2y
b)
3g + 5h + 4g - 2h
Answer:
[tex]\huge\boxed{a) 2x+7y}[/tex]
[tex]\huge\boxed{b) 7g+3h}[/tex]
Step-by-step explanation:
Part a:
= 3x + 5y - x + 2y
Combining like terms
= 3x - x + 5y + 2y
= 2x + 7y
Part b:
= 3g + 5h + 4g - 2h
Combining like terms
= 3g + 4g + 5h - 2h
= 7g + 3h
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807Find the volumes of the solids generated by revolving the regions bounded by the graphs of the equations about the given lines.
y = root x
y = 0
x = 3
the x-axis
the y-axis
the line x = 3
the line x = 6
Answer:
x-axis = [tex]\frac{9\pi }{2}[/tex]
y-axis = [tex]\frac{4\pi }{5} .3(^{\frac{5}{2} } )[/tex]
Line x =3 : [tex]\frac{44\sqrt{3} }{5} \pi[/tex]
Line x = 6 : [tex]\frac{84\sqrt{3}\pi }{5}[/tex]
Step-by-step explanation:
Given lines : y = √x
y = 0
x = 3
To determine the volumes generated we will use the disk method for each of the lines,
attached below is the detailed solution for line x =3 , same procedure will be repeated for each value of x and y to obtain the given results
The volume generated ( x axis )
= [tex]\frac{9\pi }{2}[/tex]
volume generated ( y _axis )
= [tex]\frac{4\pi }{5} .3(^{\frac{5}{2} } )[/tex]
Volume about x = 3
= [tex]\frac{44\sqrt{3}\pi }{5}[/tex]
Volume about x = 6
= [tex]\frac{84\sqrt{3}\pi }{5}[/tex]
What is the value of x in the equation shown? -4 = 5x + 3 A) -3 4/5.
B) -1 2/5
C) 1/5
D) 1 2/5
Answer:
B
Step-by-step explanation:
(8x + 11x) + (-7 - 18)
Answer:
19x - 25
steps:
(8x + 11x) + (-7 - 18)
19x + (-25)
positive x negative = negative
19x - 25
Answer:
19x - 25
Step-by-step explanation:
(8x + 11x) + (-7 - 18) <------- add the bold ones (combine like terms)...
19x + (-7 - 18) <--------------- subtract the bold ones...
(19x) - 25 <-------------------- eliminate parenthases
19x - 25 <--------------------- solution...
Jordyn is weighing the ingredients on a kitchen scale to make bread. The bowl weighs 1 1/2 pounds. He adds several scoops of flour. the total weight of the bowl and the flour is 2 3/4pounds. If each cup weighs 5/16 pound, how many cups of flour does he add?
Answer: 4 pounds of flour
Step-by-step explanation:
Show that sin( + 180°) + 2 cos( − 360°) − sin( − 180°) = 2x
Answer:
Example 1: Change sin 80° cos 130° + cos 80° sin 130° into a trigonometric function in ... Example 2: Verify that cos (180° − x) = − cos x ... Example 7: Verify that sin (360° − x) = − sin x.
Help with these ASAP
I’ve been at these questions all day. Please help
Answer:
தமிழ்நாட்டில் உள்ள நெல் வகைகளை குறிப்பிட்டு எழுதுக
Answer:
How does the novel "In Cold Blood" address the question of responsibility regarding the Clutter murders?
If a pizza pie had
a diameter of 12
inches, what
would be its
circumference?
Answer:
37.7 inches
Step-by-step explanation:
Formula of circumference:
[tex]2\pi r[/tex]
r = radius
In the current case,
radius is 6 inches
Hence,
circumference=
[tex]2*\pi *6\\= 12\pi\\= 37.6991118431[/tex]
≅ 37.7 inches
Feel free to mark it as brainliest
What is the area of the trapezoid shown below?
Answer: where is the trapezoid
Step-by-step explanation:
Help eve hehedgrhhdhrgr
Answer:
7.47
Step-by-step explanation:
Please Like and hope you have a good day get your math on!!!
60 divided by 4 - 3^2 + 2 (5)
Answer:
16
Step-by-step explanation:
Answer:
16
Step-by-step explanation:
First Step: Solve the exponent 3^2=9
Then, you get 60 divided by 4-9+2(5)
Then, you do Multiplication and Division from left to right, so 60/4=15, 2(5)=10
Then, you get 15-9+10
Then, you do addition and subtraction from left to right.
15-9=6, then 6+10=16
All the fourth-graders in a certain elementary school took a standardized test. A total of 82% of the students were found to be proficient in reading, 74% were found to be proficient in mathematics, and 65% were found to be proficient in both reading and mathematics.A student is chosen at random. What is the probability that the student is proficient in neither reading nor mathematics
Answer:
0.09 = 9% probability that the student is proficient in neither reading nor mathematics
Step-by-step explanation:
We solve this question treating the events as Venn probabilities.
I am going to say that:
Event A: A student is proficient in reading.
Event B: A student is proficient in mathematics.
A total of 82% of the students were found to be proficient in reading
This means that [tex]P(A) = 0.82[/tex]
74% were found to be proficient in mathematics
This means that [tex]P(B) = 0.74[/tex]
65% were found to be proficient in both reading and mathematics.
This means that [tex]P(A \cap B) = 0.65[/tex]
What is the probability that the student is proficient in neither reading nor mathematics?
This is:
[tex]P = 1 - P(A \cup B)[/tex]
In which
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
With the values that we have:
[tex]P(A \cup B) = 0.82 + 0.74 - 0.65 = 0.91[/tex]
Then
[tex]P = 1 - P(A \cup B) = 1 - 0.91 = 0.09[/tex]
0.09 = 9% probability that the student is proficient in neither reading nor mathematics
WILL GIVE BRAINLIST PLS HELP Find z. Just write the number. Answer should be a whole number.
Answer:
8
Step by Step Explanation
Answer and Step-by-step explanation:
To find Z, we have to use the trigonometric function of Sine.
The Sine trig function looks like this:
sin(Angle) = [tex]= \frac{opposite.side}{hypotenuse}[/tex]
Plug in the values and solve for z.
[tex]sin(30) = \frac{4}{z} \\\\\\\\\\z = \frac{4}{sin(30)}[/tex]
Plug into a calculator and solve.
We get z to be 8.
#teamtrees #PAW (Plant And Water)
Enter an algebraic expression that represents the product of r cubed and one hundred seven.
Answer:
107r³
Step-by-step explanation:
Try solving it using
An algebraic expression that represents the product of r cubed and one hundred seven is 107r³.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
We are given that represents the product of r cubed and one hundred seven.
Therefore, an algebraic expression that represents the situation
r cubed = r³
one hundred seven = 107
Thus, it would be;
107r³
Hence, an algebraic expression that represents the product of r cubed and one hundred seven is 107r³.
To know more about an expression follow;
brainly.com/question/19876186
#SPJ5
There are 15 students on the debate team. Of these, 3 are boys. Give the ratio of boys to girls on the debate team in simplest form.
Answer:
Hiya! I see this is your first question on here, I hope you enjoy the website. Anyways, the answer is 1/4 I believe.
Step-by-step explanation:
15-3=12
3 : 12
1 : 4
P.S. smile for me and have a great day!
You want to buy some groceries there is a coupon that offers a %15 discount on your total bill your bill comes to $76 how much money will you save
Answer:
$64.6
Step-by-step explanation:
15% off $76 = -$11.4 = $64.6
Calculating a Data Value from a Percentile
The total mass of raisins in a package Normally
distributed, with a mean of 520 grams and a standard
deviation of 5 grams.
Use the z-table to answer the question.
What mass would be lower than the mass of 92% of
the packages?
O 525 grams
O 530 grams
O 550 grams
O 575 grams
Answer:
525 grams
Step-by-step explanation:
Answer:
525 grams is correct
ED2021
Find the sum. Enter your answer in the box below as a fraction, using the slash mark ( / ) for the fraction bar.
2/7+3/7
Answer:
5/7
Step-by-step explanation:
2/7 + 3/7
Denominator are equal so adding numerator,
(2+3)/7 = 5/7
PLEASE HELP ASAP!!!!
Select all expressions that are equivalent to 2+y+y+y+y+y+3?
(9z+7) whats the value of z
Answer:
-0.78
Step-by-step explanation:
9z+7
9z = -7
z = -7÷9
z = -0.78
Write each product using an exponent. 9 x 9 x 9 x 9 x9
(Will be giving brainliest)
Answer: 9^ 5
Step-by-step explanation: since there is 5 9’s multiplied by each other, it would be 9 to the 5th power.
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathtt{9\times9\times9\times9\times9}\\\mathtt{= 81\times 81\times9}\\\mathtt{= 6,561\times9}\\\mathtt{= 59,049}\\\mathtt{= 9\times 9\times 9 \times 9 \times 9 \rightarrow 9^5}[/tex]
[tex]\huge\text{Therefore your answer should be:}[/tex]
[tex]\huge\boxed{\mathtt{9^5}}\huge\checkmark[/tex]
[tex]\huge\boxed{\mathtt{Good \ luck \ on \ your \ assignment\ \& \ enjoy}}\\\huge\boxed{\mathtt{your \ day!}}[/tex]
One, no, or infinitely many solutions?
Answer:
One solution
x = 3
Step-by-step explanation:
3x + 5 + 6x - 7 = 25
combine like terms:
9x -2 = 25
add 2 to each side of the equation:
9x = 27
divide both sides by n9:
x = 3
An architect’s blueprint for a new house shows the kitchen being 7 inches wide. If the scale used to create the blueprint is 0.5 in. = 1 ft, what is the actual width of the kitchen?
What is m∠1?
There is a horizontal line. Point B and D are lies on the line. There is one point C which is joined with point B and D to form a triangle CBD. The angle BCD is 70 degree. The angle CBD is denoted by 2. The supplementary angle of 2 is denoted by angle 1 which is line formed with segment BC. The line formed obtuse angle with CD is 130 degree.
A. 130°
B. 70°
C. 60°
D. 120°
Answer:
i think b
Step-by-step explanation:
Solve Similar triangles
Solve for x.
x=?
Answer:
x = 2
Step-by-step explanation:
AB/BC = AD/DE
[tex]\frac{2}{1}[/tex] = [tex]\frac{2+x}{2}[/tex]
cross-multiply:
2+x = 4
x = 2
as a medical technician, Stephanie has been offered a job that pays $53 000.00 per year and another job that pays $25.50 per hour. assuming a 40 hour work week and all other conditions being the same, at which job will she earn more?
Answer:
25.50x40= 1020/ week
times 52 weeks- $53040