The test Score of a Math class with 800 students are distributed
normally with a mean of 75 and a standard deviation of 7.
a) What percentage of a class has a test score between 68 and 82?
b) Approximately how many students have a test score between 61
and 89?
c) What is the probability that a student chosen at random has a
test score between 54 and 75?
d) Approximately how many students have a test score greater
than or equal to 96?
Answers
Answer:
(a) 68.3%
(b) 764 students
(c) 49.87%
(d) 1 student
Step-by-step explanation:
You want to know various percentages and numbers of students in different test score ranges when 800 students have scores normally distributed with a mean of 75 and a standard deviation of 7.
a) [68, 82]The range 68 to 82 is one standard deviation either side of the mean: 75±7. The "empirical rule" tells you about 68% of students will have a test score in this range. An appropriate calculator gives the fraction as 68.3%.
b) [61, 89]The range 61 to 89 is 2 standard deviations either side of the mean: 75±2·7. The "empirical rule" tells you about 95% of the 800 students will have a test score in this range. An appropriate calculator puts the number slightly higher than 760 students: 764 students.
c) [54, 75]The range 54 to 75 is 3 standard deviations below the mean. The empirical rule tells you about 99.7% of the group falls inside 3 standard deviations. Half this number is below the mean, about 49.85% An appropriate calculator puts the number slightly higher: 49.87%.
d) [96, ∞)The scores at 96 and above are more than 3 standard deviations above the mean. As in part (c), the number in that tail are given by the empirical rule as about 0.15%, or 1.2 students. An appropriate calculator puts the number in the tail of the distribution at a slightly lower value. Hence, the estimated number of students with a score at least 96 is 1 student.
__
Additional comment
The numbers in this question seem to be chosen so you can use the empirical rule to find the answers. That rule will make the answers slightly different: 68%, 760 students, 49.85%, 1 student.
a) The percentage of a class has a test score between 68 and 82 is; 68.269%
b) The number of students that will score between 61 and 89 is; 764 students
c) The probability that a student chosen at random has a test score between 54 and 75 is; 0.49865
d) The number of students that have a test score greater than or equal to 96 is; 1
How to solve normal distribution problems?We are given;
Mean; μ = 75
Standard deviation; σ = 7 ;
a) We have to find percentage of a class has a test score between 68 and 82. This is expressed as; P(68 < X < 82)
P(68 < X < 82) = P(X < 82) - P(X < 68)
The formula for z-score is;
z = (x' - μ)/(σ)
Thus;
P(68 < X < 82) = P(Z < (82 - 75)/7) - P(Z < (68 - 75/7)
P(-1<x<1) = 0.68269 = 68.269%
b) The number of students that will score between 61 and 89 is;
P(61 < X < 89)
z -scores;
z = (61 - 75)/7
z = -2
z = (89 - 75)/7
z = 2
p-value between the two z-scores from online calculator is;
p = 0.9545
Number of students here = 0.9545 * 800 ≈ 764 students
c) The probability that a student chosen at random has a test score between 54 and 75;
P(54 < X < 75)
z -scores;
z = (54 - 75)/7
z = 3
z = (75 - 75)/7
z = 0
p-value between the two z-scores from online calculator is;
p = 0.49865
d) We want to find out how many students have a test score greater
than or equal to 96.
z = (96 - 75)/7
z = 3
p-value from z-score calculator gives;
p = 0.00135
Thus;
Number of students in this regards = 0.00135 * 800 ≈ 1
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Related Questions
a whole number divided by a decimal number is a whole number
Answers
Answer:
This statement is False.
Step-by-step explanation:
It is not impossible, but on MOST occasions, you will get a decimal number.
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 15 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
Ed has a card shop. Ed’s profit on “Good Luck” cards in 2018 was . This was a decrease of on his profit in 2017. Work out Ed’s profit on “Good Luck” cards in 2017.
Answers
Ed’s profit on “Good Luck” cards in 2017 is $450.
Given that, Ed's profit on “Good Luck” cards in 2018 was £360. This was a decrease of 20% on his profit in 2017.
What is gain or profit?The profit or gain is equal to the selling price minus the cost price. Loss is equal to the cost price minus the selling price.
Let x be the profit on "Goodluck" card in 2017.
Now, x - 20% of x=360
⇒ x - 20/100 × x = 360
⇒ x - 0.2x = 360
⇒ 0.8x = 360
⇒ x = 360/0.8
⇒ x = 450
Therefore, Ed’s profit on “Good Luck” cards in 2017 is $450.
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"Your question is incomplete, probably the complete question/missing part is:"
Ed's profit on “Good Luck” cards in 2018 was £360.This was a decrease of 20% on his profit in 2017.Work out Ed's profit on “Good Luck” cards in 2017.
A large company releases summary statistics about the annual salaries for its employees. Based on the information, are there any outliers in the data? Explain your reasoning
Answers
Based on the information given; there are outliers in the data and this can be attributed to the relatively large standard deviation relative to the mean.
What are Outliers?Outliers as the name implies are data values which significantly deviate from the measures of central tendency such as mean and median.
On this note, the major outliers in the scenario are; the minimum and maximum whose values are $18,000 and $350,000 respectively.
It is noteworthy to also know that the relatively large standard deviation with respect to the mean is an indicator of the presence of outliers in the data.
Ultimately, there are outliers in the data given and this follows from the fact that the mean, Q1, Q3 all range between 50,000 - 58,000 while the outliers can register for them LAS
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Harry is training for a cross-country track event. The table shows the proportional relationship between his distance and time. Distance (miles) 0.7 1.4 ? Time (minutes) 7.7 15.4 28.6 How many miles can Harry run in 28.6 minutes? 2.6 miles 2.4 miles 2.1 miles 3 miles
Answers
With respect to the proportional relationship table, Harry can run 2.6 miles in 28.6 minutes
What is the proportional relationship?
If all of the ratios of the variables are equal, then there is a proportional link between the two variables. In a proportional relationship, one variable is, in other words, always a constant value multiplied by the other variable. In other words, a relationship is proportional if it can be explained by multiplying each pair of data values by a certain amount.
Solution Explained:
A/Q, the table shows the proportional relationship between distance and time.
Given,
Distance Time
0.7 7.7
1.4 15.4
x 28.6
We know, the ratios are equivalent in a proportional relationship
If we divide, 0.7 and 7.7, we get 11
so taking 11 as the constant of proportionality, we get
x X 11 = 28.6
x = 28.6 / 11
x = 2.6
Therefore, Harry can run 2.6 miles in 28.6 minutes.
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Answer:
Harry can run 2.6 miles in 28.6 minutes
Step-by-step explanation:
A/Q, the table shows the proportional relationship between distance and time.
Given,
Distance Time
0.7 7.7
1.4 15.4
x 28.6
We know, the ratios are equivalent in a proportional relationship
If we divide, 0.7 and 7.7, we get 11
so taking 11 as the constant of proportionality, we get
x X 11 = 28.6
x = 28.6 / 11
x = 2.6
Therefore, Harry can run 2.6 miles in 28.6 minutes.
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y = f(x-5)+3 looking for a graph
Answers
(2,0) (0, -2)
Y intercept is -2
Which descriptions from the list below accurately describe the relationship
between AQRS and ATUV? Check all that apply.
A. Congruent
B. Similar
c. Same size
D. Same sides
Answers
The two relationships between the two triangles QRS and TUV is that they are similar triangles.
Option b is correct.
What is a similar triangle?
If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are comparable.
Similar figures are described as items with the same shape but varying sizes, such as two or more figures. The polygon with three sides is a triangle. The prerequisites for a triangle's resemblance are that the corresponding angles on both triangles must be identical, and the corresponding sides must be proportional to one another.
In the given question, we have:
The two triangles: QRS and TUV;
and we have the measure of the angles;
∠Q = 76°
∠R = 26°
∠S = 76°
∠T = 76°
∠U = 26°
∠V = 76°
and the sides measure:
RQ = 4cm;
RS = 2cm;
SR = 4cm;
UT = 12cm;
TV = 6cm;
UV = 12cm;
So, when we find the proportion of the corresponding sides, we get:
The ratio of sides is as [tex]\frac{1}{2}[/tex];
and all the corresponding angles are equal;
So, we can say that the two triangles are similar;
Hence, The two triangles are similar;
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What is the image of ( − 8 , 7 ) after a dilation by a scale factor of 3 centered at the origin?
Answers
The image of (-8, 7) after dilation by a scale factor of 1/3 centered at the origin is : (-8/3, 7/3)
Given point P (-8, 7)
The point is dilated by a scale factor of 1/3 centered at the origin is equivalent to multiplying the point by 1/3 for both the co-ordinates.
Therefore, the new point is given by :
P' = (-8×(1/3), (7)×(1/3))
P' = (-8/3, 7/3)
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Given the graph of f(x), find each of the following:
f(-1), f(0), f(1), f(2), f(3)
f(x) __________ Feedback _______________
Answers
The value of the function at x = -1, 0, 1, 2, and 3 will be -4, 3, 2, -1, and 0, respectively.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
From the graph of f(x), then the value of the function at x = -1, 0, 1, 2, and 3 will be given as,
x f(x) Feedback
-1 -4 Point is in the fourth quadrant
0 3 Point is in the y-axis
1 2 Point is in the first quadrant
2 -1 Point is in the second quadrant
3 0 Point is in the x-axis
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As Mercury revolves around the sun, it travels at a rate of approximately 30 miles per second. Convert this rate to miles per minute. At this rate, how many miles will Mercury travel in 3 minutes? Do not round your answers.
Answers
The conversion of 30 miles per second into miles per minute is 1800 miles per minute and Mercury will travel 5400 miles in 3 minutes at this rate.
According to the question,
We have the following information:
Mercury travels at a rate of approximately 30 miles per second.
We know that there are 1/60 minutes in 1 second.
So, we have the following expression for conversion:
30/(1/60) miles per minute
30*60
1800 miles per minute
Now, we know that following formula is used to find distance:
Distance = speed*time
Distance = 1800*3
Distance = 5400 miles
Hence, the conversion of 30 miles per second into miles per minute is 1800 miles per minute and Mercury will travel 5400 miles in 3 minutes at this rate.
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Question 6 of 10
For what values of x is the expression below defined?
√3x²+√4x
OA. x< 1
OB. x > 0
OC. x = 0
OD. x<0
Answers
The given expression √3x²+√4x is defined for x > 0
By property |f(x)| < c
⇒ f(x) < 0 and - f(x) < 0
⇒√3x²+√4x < 0 and -(√3x²+√4x) < 0
⇒ x < -√4/3 and x < -√4/3
Therefore x should be greater than 0.
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Distribute to create an equivalent expression with the fewest symbols possible.
4(5+y) =4(5+y)
Answers
The equivalent expression of 4(5+y) by distributing is 20 + 4y.
How to find equivalent expression?In maths, an expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.).
Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.
In other words, two mathematical expressions are said to be equivalent if they yield the same result upon solving them.
Therefore, let's find the equivalent expression of 4(5 + y) by distributing it.
Hence,
4(5 + y) = 20 + 4y
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If leonardo picks 5 buckets of blueberries an hour, and his piecework rate is $15 per bucket. How much many will he make in 4 weeks of blueberry picking? He works 5 days a week, 6 hours a day.
Answers
Answer:
30 every 5 days
Step-by-step explanation:
Please answer need to turn it in please help me answer
Answers
Answer: Sir in what way would you like me to explain this
Step-by-step explanation:
Passes through (-2,6) and perpendicular to y=2x-5
Answers
Answer:
y=-1/2x + 5
Step-by-step explanation:
First, since it is perpendicular, you will change the 2x to a fraction form, -1/2x.
Now, input -2(x) and 6(y) into the respective variables.
So, you will get 6=-1/2(-2)+b
6=1
-1 -1
5=b
So, the equation will be y=-1/2x + 5
What is the slope of the
function below?
(2,5)
(4,8)
Slope =
?
Answers
Answer:
y = 3/2x + 2
Step-by-step explanation:
The x axis runs by 2.
The y axis rises/drops (depends on which you are using) by 3.
The format is rise over run.
So its 3/2
3x-2y=12
y=1 - 2x
HELPPPPP
Answers
Answer
3x−2y=12y=1−2x
re
Last week, a florist sold 715 roses. Of the
roses sold, 7 out of every 11 roses were
red. How many red roses did she sell?
Answers
The total number of red roses sold by the florist is 455.
A Fraction represents the parts of a whole or collection of objects. The first and most common form of representing a fraction is [tex]\frac{a}{b}[/tex].
Here, a is the numerator, and b is the denominator.
Number of Roses sold by The florist = 715
Fraction for the number of red roses sold = [tex]\frac{7}{11}[/tex] (7 out of 11 roses)
We have to find the number of red roses sold by the florist.
Now,
The number of red roses sold by the florist will be
[tex]\frac{7}{11} \ of\ 715[/tex]
[tex]=\frac{7}{11}*715[/tex]
[tex]=\frac{7*715}{11}[/tex]
[tex]=\frac{5005}{11}[/tex]
[tex]=455[/tex]
Hence, the total number of red roses sold by the florist is 455.
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identify the following scatter plots as having a positive correlation, negative correlation, or no correlation explain your reasoning
Answers
Answer:
Step-by-step explanation:
This diagram represents a negative correlation as the first point has a y value of 5.5 and the last point has a y-value of 2, meaning that there is a rise of -3.5, suggesting a negative correlation"
find the unit vector
Answers
Answer:
Step-by-step explanation:
Vector:
AB = { 2 - 5; 7 - 3; -1 - (-1) } = { -3; 4; 0 }
Vector modulus:
| AB | = √ ( (-3)² + 4² + 0² ) = √ (9 + 16 + 0 ) = √ 25 = 5
Unit vector:
U = -(3/5)·i + (4/5)·j + 0/5·k
U = -(3/5)·i + (4/5)·j
Solve for x
7(x-2) < 2x +3
Give your answer as an improper fraction in its simplest form.
Answers
Answer:
[tex]x < \frac{17}{5}[/tex]
Step-by-step explanation:
Take a look at the attachment...
Hope this helps! :)
arch
Convert the following equation
into slope-intercept form.
-8x + y = -9
0
y = [? ] x + [
Answers
Slope-intercept form is −8x+9. One of the formulas used to get a line's equation is the slope-intercept formula.
What is Slope-intercept form ?Slope-intercept is a specific form of linear equations. The equation of the line is written in the slope-intercept form, which is: y = mx + b, where m represents the slope and b represents the y-intercept. In our equation, y = − 3 x + 5 , we see that the slope of the line is − 3 .
A method of formulating a line's equation that makes it simple to identify the slope and y-intercept is known as the slope-intercept form. The y-intercept, or point where the line crosses the y-axis, is where the slope, or steepness, of the line is located.
-8x + y = -9
move y to right side
-8x = -9-y
Divide both sides by -8
-8x/-8x = -(9/-8) - (y/-8)
Simplify
-8x/-8x = -(9/-8) - (y/-8)
Simplify -8x/-8x : x
Simplify -(9/-8) - (y/-8) : -9 - y / 8
x = -(-9 - y / 8)
y = mx + b.
y = −8x+9
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IXL Help Fast Please !
Answers
Answer:9-0
Step-by-step explanation:sdwew
Answer:
x = 35 degrees
Step-by-step explanation:
3x-11+2x+16 = 180
5x +5 = 180
5x = 180 -5
5x = 175
5/5 x = 175/5
x = 35 degrees
Look in the photo
Use the chart to find h(4) in simplest form
Answers
By using the given chart, the value of h'(4) would be -16.
What is a chain rule in calculus?
According to the chain rule, the derivative of f(g(x)) is f'(g(x)).g' (x). In other words, it aids in the differentiation of 'composite functions'.
Sin(x²), for example, is a composite function because it can be written as f(g(x)) where f(x)=sin(x) and g(x)=x².
The given function is
h(x) = f(g(x))
Now differentiating the above function with respect to x, we get
h'(x) = f'(g(x)) * g'(x)
Now find h'(4), so put x = 4, we get
h'(4) = f'(g(4)) * g'(4)
By using the given table, we can write
h'(4) = f'(-1) * 8
h'(4) = (-2) * 8
h'(4) = -16
Hence, by using the given chart, the value of h'(4) would be -16.
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Find the length of the curve
y=e^x, 0≤x≤ 1.
Answers
The length of the curve is 2.0036.
The equation of the curve is y = e^(x). The interval is 0 ≤ x ≤ 1. A curve is a smoothly drawn figure or line in a plane that has a bend or twist in it. A curve is defined as a continuous and smooth flowing line with no sudden twists. A curve is an abstract concept in mathematics that describes the path of a continuously moving point. The arc length of a curve y = f(x) in the increasing interval from a to b is given below.
[tex]L = \int\limits^a_b {\sqrt[]{ 1 + (\frac{dy}{dx})^{2}} \, dx[/tex]
dy/dx = d(e^x)/dx = e^x
(dy/dx)² = e^(2x)
The length of the given curve is calculated below.
[tex]L = \int\limits^1_0 {\sqrt[]{ 1 + e^{2x}}, dx[/tex]
L = [√(1+e^2x) + (1/2)ln(√(1+e^2x) - 1) - (1/2)ln(1 + √(1+e^2x))] from limits 0 to 1.
L = [√(1+e²) + (1/2)ln(√(1+e²) - 1) - (1/2)ln(1 + √(1+e²))] - [√(1+1) + (1/2)ln(√(1+1) - 1) - (1/2)ln(1 + √(1+1))]
L = [√(1+e²) + (1/2)ln(√(1+e²) - 1) - (1/2)ln(1 + √(1+e²))] - [√2 + (1/2)ln(√2 - 1) - (1/2)ln(1 + √2)]
L ≈ 2.0036
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Bruce wants to make 50 ml of an alcohol solution with a 12% concentration. He has a 10% alcohol solution and a 15% alcohol solution. The equation 0.10x + 0.15(50 – x) = 0.12(50) can be used to find the amount of 10% alcohol solution Bruce should use.
How much of the 10% alcohol solution should Bruce use?
__ mL
How much of the 15% alcohol solution should Bruce use?
__mL
Answers
x = 10% solution
y = 15% solution
let's start at the beginning, without the equation just yet, so let's start off by making a table for the substances and let's use the decimal format for the percentages to get the actual amounts.
[tex]\begin{array}{lcccl} &\stackrel{mL}{quantity}&\stackrel{\textit{\% of mL that is}}{\textit{alcohol only}}&\stackrel{\textit{mL of}}{\textit{alcohol only}}\\ \cline{2-4}&\\ \textit{10\% sol'n}&x&0.10&0.10x\\ \textit{15\% sol'n}&y&0.15&0.15y\\ \cline{2-4}&\\ mixture&50&12&6 \end{array}~\hfill \begin{cases} x + y = 50\\\\ 0.10x+0.15y=6 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{using the 1st equation}}{x+y=50\implies y=50-x}\hspace{5em}\stackrel{\textit{substituting on the 2nd equation}}{0.10x+0.15(\underset{y}{50-x})=6} \\\\\\ 0.10x+7.5-0.15x=6\implies -0.05x+7.5=6\implies -0.05x=-1.5 \\\\\\ x=\cfrac{-1.5}{-0.05}\implies \boxed{x=30}\hspace{15em}\stackrel{50~~ - ~~30}{\boxed{y=20}}[/tex]
Which equations are true equations? Select all correct answers. Responses 39−3⋅6=6⋅104+4 39 minus 3 times 6 equals fraction numerator 6 times 10 over denominator 4 end fraction plus 4 82−52=42−7 8 squared minus 5 squared equals 4 squared minus 7 56÷8+32=2⋅23 56 divided by 8 plus 3 squared equals 2 times 2 cubed 2422=50−62−8
Answers
The equation 56 ÷ 8 + 3² = 2⋅2³ is true which is the correct answer would be option (C).
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
As per option (A),
39 − 3⋅6 = 6⋅10/4 + 4
39 - 18 = 6 × 5/2 + 4
11 = 30/2 + 4
11 = 15 + 4
11 = 19
This equation is not true.
As per option (B),
8²−5²=4²−7
64 - 25 = 16 - 7
39 = 9
This equation is not true.
As per option (C),
56 ÷ 8 + 3² = 2⋅2³
56 / 8 + 9 = 2 × 8
7 + 9 = 16
16 = 16
This equation is true.
Therefore, the equation 56 ÷ 8 + 3² = 2⋅2³ is true.
Hence, the correct answer would be option (C).
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O and R are the subsets of a Universal set, U, such that U={22,23,24,25,26,27,28,29,30} 0={ prime numbers } {R}={ even numbers } a) Draw a Venn diagram to represent this information.
b) List the elements of.
i) ( O U R )'
ii) ( O ∩ R)'
iii) O ∩ R
Answers
The elements of (OUR)', (O∩R)', and O∩R will be {23, 29}, {22, 23, 24, 26, 28, 29, 30}, and {null}, respectively.
What are Sets?Sets are groups of clearly specified components. The number of items in a finite set is denoted by a curly bracket.
O and R are the subsets of a Universal set, U, such that
U = {22,23,24,25,26,27,28,29,30}
O = {prime numbers} = {23, 29}
R = {even numbers} = {22, 24, 26, 28, 30}
The elements of (OUR)' will be given as,
(OUR)' = {23, 29}
The elements of (O∩R)' will be given as,
(O∩R)' = {22, 23, 24, 26, 28, 29, 30}
The elements of O∩R will be given as,
O∩R = 0
The elements of (OUR)', (O∩R)', and O∩R will be {23, 29}, {22, 23, 24, 26, 28, 29, 30}, and {null}, respectively.
The Venn diagram is given below.
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How do you simplify ((-3)2)3.
Answers
Answer: -18
Step-by-step explanation:
((-3)2)3
((-3) x 2) x 3
Apply rule (-a) = - a
(-3) = -3
-3 x 2 x 3
-6 x 3
= -18
5 candy bars with 12 sections split between 3 friends equally
Answers
Answer:
20 sections per friend
Step-by-step explanation:
First find the total number of sections
5 * 12 = 60 sections
Divide by 3 friends
60/3 = 20
20 sections per friend
The perimeter of a triangle is 51 meters.The second side is twice as long as the first. The third side is 3 meters less than three times the first. What is the length of the second side of the triangle?
Answers
The length of the second side of the triangle is 18 m
What is the perimeter of a Triangle?
The perimeter of a triangle is given by the formula
Perimeter of a triangle = Sum of all three sides
Let the sides of the triangle be a , b , c
Perimeter of a triangle = a + b + c
Given data ,
Perimeter of the triangle = 51 m
Let the first side , second side and third side of the triangle be a , b and c respectively
So , a + b + c = 51 m
And , The second side is twice as long as the first
So , b = 2a
And , The third side is 3 meters less than three times the first
So , c = 3a - 3
Substituting the values of a , b and c in the perimeter equation , we get
a + 2a + 3a - 3 = 51
6a - 3 = 51
Adding 3 on both sides , we get
6a = 54
Divide by 6 on both sides , we get
a = 9 m
Substituting the value of a , we get
b = 2a
b = 2 x 9
b = 18 m
c = 3a - 3
c = 3 x 9 - 3
c = 27 - 3
c = 24 m
So the length of the first side , second side and third side is 9m , 18 m and 24 m respectively
Hence , the length of the second side is 18 m
To learn more about perimeter of triangle :
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