The test scores on a 100-point test were recorded for 20 students:71 93 91 86 7573 86 82 76 5784 89 67 62 7277 68 65 75 84a. Can you reasonably assume that these test scores have been selected from a normal population? Use a stem and leaf plot to justify your answer.b. Calculate the mean and standard deviation of the scores.c. If these students can be considered a random sample from the population of all students, find a 95% confidence interval for the average test score in he population.
Answers
Answer: a. Yes
b. mean = 76.65
standard deviation = 10.04
c. 76.65 ± 4.4
Step-by-step explanation:
a. Stem and leaf Plot shows the frequencies with which classes of value occur. To create this plot, we divide the set of numbers into 2 columns: stem, the left column, which contains the tens digits; leaf, the right column, which contains the unit digits.
Normal distribution is a type of distribution: it's a bell-shaped, symmetrical, unimodal distribution.
A stem and leaf plot displays the main features of the distribution. If turned on its side, we can see the shape of the data.
The figure below shows the stem and leaf plot of the 100-point test score. As we can see, when turned, the plot resembles bell-shaped distribution. So, this test scores were selected from a normal population.
b. Mean is the average number of a data set. It is calculated as the sum of all the data divided by the quantity the sample has:
mean = [tex]\frac{\Sigma x}{n}[/tex]
For the 100-point test score:
mean = [tex]\frac{71+93+91+...+65+75+84}{20}[/tex]
mean = 76.65
Standard Deviation determines how much the data is dispersed from the mean. It is calculated as:
[tex]s=\sqrt{\frac{\Sigma (x-mean)^{2}}{n-1} }[/tex]
For the 100-point test score:
[tex]s=\sqrt{\frac{[(71-76.65)+(93-76.65)+...+(84-76.65)]^{2}}{20-1} }[/tex]
s = 10.04
The mean and standard deviation of the scores are 76.65 and 10.04, respectively.
c. Confidence Interval is a range of values we are confident the real mean lies.
The calculations for the confidence interval is
mean ± [tex]z\frac{s}{\sqrt{n} }[/tex]
where
z is the z-score for the 95% confidence interval, which is equal 1.96
Calculating interval
76.65 ± [tex]1.96.\frac{10.04}{\sqrt{20} }[/tex]
76.65 ± 4.4
The 95% confidence interval for the average test score in the population of students is between 72.25 and 81.05.
Related Questions
solve 10x + 5y = 9 for y
Answers
Answer:
y= 9-10X/5
Step-by-step explanation:
Plz make me braibliest
Answer:
10x+5y=9 years
or,15xy=9 years
or,xy=15÷9
Ans=6xy.
The area of a rectangle is 1260 square inches. Its length is 36 inches.
Find the width
Answers
4, 20, 100, 500, what’s the next number?
Answers
4, 20, 100, 500, 2500
Answer:
2500
Step-by-step explanation:
multiply by 5 every time
The electric-vehicle manufacturing company Tesla estimates that a driver who commutes miles per day in a Model S will require a nightly charge time of around hour and minutes ( minutes) to recharge the vehicle's battery (Tesla company website). Assume that the actual recharging time required is uniformly distributed between and minutes.
A. Give a mathematical expression for the probability density function of battery recharging time for this scenario.
B. What is the probability that the recharge time will be less than 110 minutes?C. What is the probability that the recharge time required is at least 100 minutes?D. What is the probability that the recharge time required is between 95 and 110 minutes?
Answers
Answer:
Following are the solution to the given points:
Step-by-step explanation:
Please find the complete question in the attached file.
In this question, we assume that "x" denotes as an actual time of the battery charging, that is a uniform random variable that [tex]x \sim U(90, 120)[/tex]
In point a:
so, pdf of x =
[tex]\to f(x)= \frac{1}{120-90} = \frac{1}{30} \\\\\to 90 < x <120[/tex]
In point b:
To find
[tex]\to P(x<110) = \int^{110}_{90} \frac{1}{30} \ dx\\\\=\frac{110-90}{30}\\\\=\frac{20}{30}\\\\=\frac{2}{3}\\\\[/tex]
In point c:
[tex]\to P(x<100) = \int^{100}_{90} \frac{1}{30} \ dx \\\\= \frac{100-90}{30}\\\\= \frac{10}{30}\\\\= \frac{1}{3}\\\\[/tex]
In point d:
[tex]\to P(95< x< 110)[/tex]
[tex]= \int^{110}_{95} \frac{1}{30} \ dx\\\\= \frac{110-95}{30} \\\\= \frac{15}{30} \\\\= \frac{1}{2}[/tex]
You are purchasing Cotton swabs that come in 2 different sized containers. One box contains 300 swabs for 2.99 and the other box is specially marked at 30% more swabs for the same price. How much will you save per sawn by buying the larger box?
Answers
Answer:
Buying the larger box, I will be saving 23% compared to the original price.
Step-by-step explanation:
Given that a box contains 300 swabs for 2.99 and the other box is specially marked at 30% more swabs for the same price, to determine how much will I save per swab by buying the larger box the following calculation must be performed:
2.99 / 300 = X
0.0099 = X
2.99 / (300 x 1.3) = X
2.99 / 390 = X
0.0076 = X
0.0099 = 100
0.0076 = X
(0.0076 x 100) / 0.0099 = X
77 = X
100 - 77 = 23
Therefore, buying the larger box I will be saving 23% compared to the original price.
a truck just left the weigh station on interstate 40. it weighted 6 tons 500 pounds and had a load of 1,200 pounds. How much would the transfer truck alone weigh?
Answers
Answer:
The weight limit on the bridge is75,500 pounds. ... In pounds, how much cargo can the truck carry and still be ... Helllppp pleaseeee A rancher has a three sided plot of ..
Which function shows a positive rate of change?
Answers
Answer: C
Step-by-step explanation:
C. because rate of change is the slope aka y/x. The other answers give off negative slopes when determining y/x.
Halla el MCM de 3 y 5 enumerando múltiplos.
A. 15
B. 35
C. 53
D. 8
E. Ninguno de los anteriores
Answers
Answer:
A. 15
Step-by-step explanation:
Mínimo Común Múltiplo (MCM)
El MCM entre dos o más enteros es el menor múltiplo común a todos ellos. Por ejemplo, el MCM de 20 y 30 es 60 porque es el menor múltiplo común a ambos números.
El MCM entre 3 y 5 se puede determinar listando los múltiplos de cada uno:
Múltiplos de 3: 3, 6, 9,12, 15, 18, 21, 24
Múltiplos de 5: 5, 10, 15, 20, 25, 30
Se puede observar que el primer múltiplo que aparece en ambas listas en 15, luego la respuesta es:
A. 15
Tina is 4 times older than Hanna. The sum of their ages is 40. How old is Hanna?
Answers
Answer:
Hanna is 8 years old.
Step-by-step explanation:
Hanna = x
Tina = 4x
Sum = 40.
Hanna =?
Hanna + Tina = 40
4x + x = 40
5x = 40
x = 40/5
x = 8.
Hanna is 8 years old.
Find 47.5% of 690 (remember this is a non calculator question)
Answers
Answer:
327.75
Step-by-step explanation:
Find the volume of the Triangular Prism
Volume
Answers
Answer:
Volume = 144 m³
Step-by-step explanation:
Volume of triangular prism = ½*b*h*l
Where,
Base of triangular base (b) = 4 m
Height of triangular base (h) = 12 m
Length of prism (l) = 6 m
Volume = ½*4*12*6
Volume = 2*12*6 = 144 m³
Answer:
144cm3 is the right answer
Step-by-step explanation:
Oooooooooooooooooofffffffffffffffffffff
Suppose that f (x) = 1.5x2 for -1 < x < 1 and f (x) = 0 otherwise. Determine the following probabilities.
a. P(0 < X)
b. P(0.5 < X)
c. P(-0.5 = X = 0.5)
d. P(X<-2)
e. P(X < 0 or X>-0.5)
f. Determine x such that P(x < X) = 0.05.
Answers
Answer:
a) P(0 < X) = 0.5
b) P(0.5 < X) = 0.4375
c) P(-0.5 = X = 0.5) = 0.125
d) P(X< -2) = 0
e) P(X < 0 or X>-0.5) = 1
f) value of x is -0.9654
Step-by-step explanation:
Given that;
f(x) = 1.5x²
Now. the probabilities would be the integral of the given function from (-1 to 1)
a) P(0 < X)
P(X > 0)
⇒ Integral from 0 to 1 of f(x)
= (1/2)x³
= 1/2 - 0
= 0.5
Therefore; P(0 < X) = 0.5
b) P(0.5 < X)
P(X > 0.5)
this will also be done in the same way except that, the limits changes to { 0.5 to 1]
= (1)³/2 - (0.5)³ /2
= 0.4375
Therefore; P(0.5 < X) = 0.4375
c) P(-0.5 = X = 0.5)
The limits become [-0.5 , 0.5]
= (0.5)³/2 - (-0.5)³/2
= 0.125
Therefore; P(-0.5 = X = 0.5) = 0.125
d) P(X<-2)
since value of f(x) = 0 in that region
Therefore P(X< -2) = 0
e) P(X < 0 or X>-0.5)
= P(X < 0) + P(X > -0.5) - P( -0.5 < X < 0 )
= 0.5 + 0.5625 - 0.0625
= 1
Therefore; P(X < 0 or X>-0.5) = 1
f) Determine x such that P(x < X) = 0.05.
Let the value be 'a'
Then, integral from -1 to a will = 0.05
a³ - (-1)³ = 0.05 × 2
a³ + 1 = 0.10
a³ = 0.10 - 1
a³ = -0.9
a = ∛-0.9
a = -0.9654
Therefore, value of x is -0.9654
a) P(0 < X) = 0.5
b) P(0.5 < X) = 0.4375
c) P(-0.5 = X = 0.5) = 0.125
d) P(X< -2) = 0
e) P(X < 0 or X>-0.5) = 1
f) value of x is -0.9654
Determine the following probabilities:a) P(0 < X)
P(X > 0)
⇒ Integral from 0 to 1 of f(x)
[tex]= (1\div 2)x^3\\\\= 1\div2 - 0[/tex]
= 0.5
So; P(0 < X) = 0.5
b) P(0.5 < X)
P(X > 0.5)
Now
[tex]= (1)^3\div 2 - (0.5)^3 \div2[/tex]
= 0.4375
Therefore; P(0.5 < X) = 0.4375
c) P(-0.5 = X = 0.5)
The limits become [-0.5 , 0.5]
[tex]= (0.5)^3\div 2 - (-0.5)^3\div 2[/tex]
= 0.125
Therefore; P(-0.5 = X = 0.5) = 0.125
d) P(X<-2)
since value of f(x) = 0 in that region
Therefore P(X< -2) = 0
e) P(X < 0 or X>-0.5)
= P(X < 0) + P(X > -0.5) - P( -0.5 < X < 0 )
= 0.5 + 0.5625 - 0.0625
= 1
Therefore; P(X < 0 or X>-0.5) = 1
f) Determine x such that P(x < X) = 0.05.
Let us assume the value be 'a'
So, integral from -1 to a will = 0.05
[tex]a^3 - (-1)^3 = 0.05 \times 2\\\\a^3 + 1 = 0.10\\\\a^3 = 0.10 - 1\\\\a^3 = -0.9\\\\a = \sqrt[3]{-0.9}[/tex]
a = -0.9654
Therefore, the value of x is -0.9654
Learn more about the probabilities here: https://brainly.com/question/24710931
Daniel wants to buy a used car to get back and forth to work
Answers
Answer:
thats good on daniel it will save him time.
Answer:
Yea it will save him time
Step-by-step explanation:
There's no question so...
How much simple interest would $1,000 earn in 275 days at an Interest rate of 4.21%
Answers
The graph shows the location of P in point hour. Point are is on the Y axis and has the same Y coordinate of point PPoint Q is graft at (N, -2). The distance from P to Q is equal to the distance from P point R. What is the distance from point P to point Q? What is the value of N? Explain how you determine the distance from point B to point Q, and the value in. The graph shows the location of P in point R. Point are is on the Y axis and has the same Y coordinate of point P
Answers
Answer:
I cant understand read ur lesson and ask help from ur teacher
#CarryOnLearning
A Furniture maker used 9/10 of a can of paint to paint 9 chairs. she used the same amount of paint for each chair. How many cans of paint did she use for each chair in
Answers
Answer:
The person used 1/10 (one tenth) of the can to paint one chair.
Step-by-step explanation:
If she used 9/10 of the can to paint 9 chairs using same amount with each, then for each chair she used:
9/10 divided by 9 = 9/10 * 1/9 = 1/10 of the can.
Solve for X in 4^x + 6^x = 9^x
Answers
Answer:
4^x + 6^x = 9^x
9^x=9^x
x=x
What method can you use to find the area of the
composite figure? Check all that apply.
decompose the figure into one rectangle and one
triangle, and add the areas
decompose the figure into two trapezoids, and add
the areas
find the area of the larger rectangle, then subtract
the area of the square
find the area of the larger rectangle, then subtract
the area of the two small triangles
O find the area of the larger rectangle
Answers
To find the area of the composite figure:-
We can use following methods-
1. Decompose the figure into one rectangle and one triangle and add the area.
2. Decompose the figure into two trapezoids and add the area.
3. Find the area of the larger rectangle, then subtract the area of the two small triangle
What is composite figure?"It is shape that is made up of two or more geometric shapes"
What is area of triangle?A = 1/2 × b × h
where b is the base of the triangle and 'h' is the height of the triangle
What is the area of rectangle?A = l × w
where l = length of the rectangle
w = width of the rectangle
For given example,
We need to find the area of the composite figure.
To find the area of the composite figure:-
We can follow-
1. Decompose the figure into one rectangle and one triangle and add the area.
2. Decompose the figure into two trapezoids and add the area.
3. Find the area of the larger rectangle, then subtract the area of the two small triangle
Learn more about the area of composite figure here:
https://brainly.com/question/27234680
#SPJ2
Answer: A, B, and D
Step-by-step explanation:
Find the slope of the line that contains (4, 8) and (3, 1).
Answers
Answer
Step-by-step explanation:
yl grafica
Answer:
The slope would be -7
Step-by-step explanation:
To find the slope, you find two points on a line and find the difference between x-values and y-values. Then divide the difference of y-values by the difference of x-values to acquire the slope. [tex]\frac{8-1}{-4+3}[/tex] = [tex]\frac{7}{-1}[/tex] or -7, so that would be the slope.
If -4 ( 5x - 1) = 196, what is x?
Answers
Answer:
10
Step-by-step explanation:
divide each side by -4
5x-1=-49
5x=50
x=10
x = -9.6
Explanation:
First you the distributive property. -4(5x)=-20x and -4(-1)=4. Now we have -20x + 4 = 196. To single out the variable we subtract 4 from both sides. 4 - 4 = 0 and 196 - 4 = 192, now we have -20x = 192. Finally divide by -20 on both sides, -20 ÷ -20 = 1, 1x is the same as x. 192 ÷ -20 = -9.6. There your have it.
-4(5x - 1)= 196, x = -9.6.
Here is a list of numbers
13 14 18 23
18 23 30 36
From the numbers in the list, write down
the multiple of 4 and
the factor of 28
Answers
Answer:
multiple of4is 36 and factor of 28 is 14
hope it helps you
Answer:
The multiple of 4 is 36 and the factor of 28 is 14Step-by-step explanation:
The multiples of 4 : 4,8,12,16,20,24,28, 32, 36, 40, 44, 48,.....
The factors of 28 : 1,2,4,7,14 and 28
I hope it helps
Emily made 20 basketball free throws and made 13 of them. What is the experimental probability of Emily making a basket?
What is the probability that Emily doesn’t make a basket?
Answers
number made / number attempted = 13/20
number missed / number attempted = (20-13)/20 = 7/20
An iPhone costs £799 in London, €850 in Paris and $970 in New York.
Using £1 = €1.17 and £1 = $1.42, state the lowest price of the iPhone in £.
Give your answer to 2 dp.
please answer for heart, comment, 5 star rating, and brainliest
Answers
Answer:
£683.10 in New York.
Step-by-step explanation:
Given the following data;
iPhone costs in London = £799
iPhone costs in Paris = €850
iPhone costs in New York = $970
£1 = €1.17 and £1 = $1.42
First of all, to find the cheapest (lowest) price for the three phones we would have to convert the prices to Pounds (£).
a. iPhone costs in London = £799
b. iPhone costs in Paris = €850
To find the price in Pounds (£);
£1 = €1.17
iPhone costs in Paris = €850/€1.17
iPhone costs in Paris = £726.50
c. iPhone costs in New York = $970
To find the price in Pounds (£);
£1 = $1.42
iPhone costs in New York = $970/$1.42
iPhone costs in New York = £683.10
Therefore, the lowest price for the iPhone is £683.10
g(m) = m3 - 10m² + 25m + 2 at m = 6.
Answers
Answer:
G(6) = -190
Step-by-step explanation:
G(6) = (6 *3) - [10*(6)^2] + 25(6) + 2
G(6) = 18 -360 + 150 + 2
G(6) = -190
Please help with my question
Answers
Answer:
Your answer is "C"
Step-by-step explanation:
Dont ask me how I know, I just know
No clue why but brainly said I had inappropriate words in my answer so here's a picture
What is the area of this figure?
2 yd
3 yd
4 yd
7 yd
4 yd
6 yd
square yards
Please helpp
Answers
Answer:
4032 square yards
Step-by-step explanation:
Area is multiplying the numbers together. Like if you were to find the area of a rectangle, you would need to multiply the length and width together. Don't forget to add a label at the end for more credit, such as square yards.
PLS HELP I WILL BRAINLIEST 15 PTS
An ice cream truck sells ice cream between 2 p.m. and 10 p.m. each night in the summer. At the end of the night, the driver calculates his profits and makes a graph to analyze the data. What is the average rate of change for the data from the 2nd hour to the 6th hour? Be sure to include the correct units of measurement.
a scatter plot with x axis labeled Hour and y axis labeled Money Earned in Dollars per Hour with points at 1 comma 54 and 2 comma 58 and 3 comma 64 and 4 comma 78 and 5 comma 96 and 6 comma 126 and 7 comma 99 and 8 comma 75
17 hours
68 dollars
17 dollars per hour per hour
68 dollars per hour per hour
Answers
Answer:
17
Step-by-step explanation:
A slope is also known as the gradient of a line. The correct option is C, 17 dollars per hour.
What is Slope?A slope is also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.
The average rate of change for the data from the 2nd hour to the 6th hour is,
Average rate = ($126 - $58)/(6 hour - 2 hour)
= 68/4 dollar per hour
= 17 dollars per hour
Hence, The average rate of change for the data from the 2nd hour to the 6th hour is 17 dollars per hour.
Learn more about Slope of Line:
https://brainly.com/question/14511992
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Suppose a - b = 0Which one of these expressions equals ab?
A. 2a
B. 0
C. b^2
D. 2b
E. a/b
Answers
If a-b=0, a=b, so ab=bb=b^2
Answer:
b^2
Step-by-step explanation:
a - b = 0
Add b to each side
a-b+b = 0+b
a=b
We want to find ab
Replace a with b
b*b
b^2
What is the value of z?
Answers
Answer:
27°
Step-by-step explanation:
117-90=27°
27
sorry for bad sketching
Which of these sequences are arithmetic? Check all that apply.
–5, –3, 3, 13, 27, .
0, 1/4, 1/2, 3/4, 1, . . .
7, 14, 28, 56, 112, . . .
27, 40, 53, 66, 79, . . .
1, 2, 4, 8, . . .