3. The grade-point averages of 20 college seniors selected at random from a graduating class are as follows:
3.2, 1.9 ,2.7, 2.4, 2.8, 2.9, 3.8, 3.0, 2.5, 3.3, 1.8, 2.5, 3.7, 2.8, 2.0, 3.2, 2.3, 2.1, 2.5, 1.9 Calculate the standard deviation.
Answers
The standard deviation of the grade points average of the college seniors is 0.57.
The given parameters:
3.2, 1.9 ,2.7, 2.4, 2.8, 2.9, 3.8, 3.0, 2.5, 3.3, 1.8, 2.5, 3.7, 2.8, 2.0, 3.2, 2.3, 2.1, 2.5, 1.9
The sum of the given data is calculated as follows;
∑x = 3.2 + 1.9 + 2.7 + 2.4 + 2.8 + 2.9 + 3.8 + 3.0 + 2.5 + 3.3 + 1.8 + 2.5 + 3.7 + 2.8 + 2.0 + 3.2 + 2.3 + 2.1 + 2.5 + 1.9
∑x = 53.3
The mean of the distribution is calculated as follows;
[tex]\bar x = \frac{\Sigma x}{N} \\\\\bar x = \frac{53.3}{20} \\\\\bar x = 2.665[/tex]
The square of the difference between the grade point and the mean;
[tex]\Sigma (x - \bar x)^2 = (3.2- 2.665)^2 + (1.9-2.665)^2 + (2.7- 2.665)^2 + (2.4-2.665)^2 \\\\+(2.8-2.665)^2 +(2.9 - 2.665)^2 + (3.8 - 2.665)^2 + (3-2.665)^2+ \\\\(2.5 -2.665)^2 + (3.3 - 2.665)^2 + (1.8-2.665)^2 + (2.5 - 2.665)^2 + \\\\(3.7-2.665)^2 + (2.8 - 2.665)^2 + (2-2.665)^2 + (3.2-2.665)^2 + \\\\(2.3 - 2.665)^2 + (2.1-2.665)^2 + (2.5-2.665)^2 + (1.9 - 2.665)^2\\\\\Sigma (x - \bar x)^2 = 6.5055[/tex]
The standard deviation of the grade points is calculated as follows;
[tex]\sigma = \sqrt{\frac{\Sigma (x-\bar x)^2}{N} } \\\\\sigma = \sqrt{\frac{6.5055}{20} } \\\\\sigma = 0.57[/tex]
Thus, the standard deviation of the grade points average of the college seniors is 0.57.
Learn more about standard deviation here: https://brainly.com/question/12402189
Related Questions
Perimeter of piecewise rectangular figure. Please help.
Answers
Check the picture below.
so the perimeter is 6+16+14+7+8+9 = 60.
In an old photograph, the height of grandma's table is 3.8 cm. The table doesn't exist anymore; grandma doesn't know what happened to it. She does still have the vase in the photograph which is 0.8cm tall in the photograph and 30 cm tall in real life. Using the vase for a scale factor, how tall was the table? PLEASE ACTUALLY ANSWER AND DON'T JUST PUT I DON'T KNOW OKAY?
Answers
Answer:
5.67
Step-by-step explanation:
The scale factor of the height of the image is 7.89.
What is the scale factor?The scale factor is defined as the proportion of the new image's size to that of the previous image. The scale factor is the ratio of the actual size to the scaled size of the object.
Dilation is the process of increasing the size of an object while maintaining its shape. Depending on the scale factor, the object's size can be increased or decreased.
Given that In an old photograph, the height of grandma's table is 3.8 cm. The table doesn't exist anymore; grandma doesn't know what happened to it. She does still have the vase in the photograph which is 0.8cm tall in the photograph and 30 cm tall in real life.
The scale factor will be calculated as,
Scale factor = ( 30 / 3.8)
Scale factor = 7.89
To know more about scale factors follow
https://brainly.com/question/25722260
#SPJ2
8 to the 2 power-28/4+2?
Answers
Answer:
59
Step-by-step explanation:
hope it helps brainliest pls
Sin2A+Sin2B÷Sin2A-Sin2B=Tan(A+B)÷Tan(A-B) Prove that
Answers
Take L.H.S sin2A+sin2B/sin2A-sin2B
= sin2A+sin2B/sin2A-sin2B
Put
[sinC+sinD = 2sin(C+D)/2cos(C-D)/2]
[sinC-sinD = 2cos(C+D)/2.sin(C-D)/2]
= 2 sin(2A+2B)/2 cos(2A-2B)/2 / 2 cos(2A+2B) sin(2A-2B)
= sin(A+B).cos(A-B)/cos(A+B).sin(A-B)
= sin(A+B)/cos(A+B) . cos(A-B)/sin(A-B)
= tan(A+B).cot(A-B)
= tan(A+B).1/tan(A-B)
= tan(A+B)/tan(A-B)
∴ Hence we proved sin2A+sin2B/sin2A-sin2B=tan(A+B)/tan(A-B)
Two researchers, Justin and Henry, work together to study what proportion of subjects have a certain genotype in the population. They each collect a simple random sample and they find that the sample proportion is 0.70. When they construct a confidence interval based on this sample proportion, Henry comes up with (0.632, 0.768) while Justin gets (0.652, 0.788). Indicate which interval has to be wrong and why.
Answers
Using confidence interval concepts, it is found that Justin is wrong, as his interval is not symmetric about the sample proportion of 0.7.
A confidence interval has two bounds, a lower bound and an upper bound. A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds. The margin of error is the difference between the two bounds, divided by 2.In this problem, the point estimate is of 0.7.
Henry's interval is symmetric, as [tex]0.768 - 0.7 = 0.7 - 0.632[/tex].Justin's is not, as [tex]0.788 - 0.7 \neq 0.7 - 0.652[/tex].Hence, Justin is wrong, as his interval is not symmetric about the sample proportion of 0.7.
For more on confidence intervals, you can check https://brainly.com/question/25822483
explain how you your answer
Answers
Answer:
1.43 = x
Step-by-step explanation:
Math in the picture attached. Hope it helps!
A sports analyst determines that the number of points
scored in a basketball game is related to the number of
shots taken during the game. The least-squares
regression line is ý = 5.0 + 1.2x where y is the
predicted number of points scored and x is the number
of shots taken
In one game, a team takes 50 shots and scores 75
points. What is the residual for this team during this
game?
D-33
4 5
10
65
Answers
Answer:
its 10 :)
Step-by-step explanation:
Number of points scored in a basketball game is related to the number number of shots taken during the game as below:
According to questionX=number of shots taken
Y=number of points scored
Given,
X=50
Y=75
As relation given,
Y=5.0+1.2×X
When x is 50 Y= 5+1.2×50=65
∴The residual score for his team during the game is= 75-65
⇒10
Learn more about linear relation here: brainly.brainly.com/question/6691346
#SPJ2
3 bags of dog food cost $6.75 How much would they spend on 2 bags of dog food?
Answers
Answer:
$4.50 for 2 bags of dog food
Step-by-step explanation:
To find the cost of 2 bags of dog food, we first need to divide $6.75, the cost of 3 bags, by 3, to find the cost of one.
$6.75 / 3 = $2.25
Now that we know the cost of one bag, we can multiply the cost by two to find the cost of 2 bags.
$2.25 * 2 = $4.50
$4.50 for 2 bags of dog food
6x +16 >=51 kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk
Answers
Answer:
5.83333333
Step-by-step explanation:
6x + 16 = 51 (If that is what you actually intended to put)
6x + 16 - 16 = 51 -16
6x/6 = 35/6
x=5.83333333
HELPPPPP please its worth 50
Answers
[tex](3 {m}^{6} {n}^{2} ) ^{3} .2m {n}^{4} \\ = {3}^{3} {m}^{6 \times 3} {n}^{2 \times 3} \times 2 m{n}^{4} \\ = 27 {m}^{18} {n}^{6} \times 2m {n}^{4} \\ = (27 \times 2) {m}^{18 + 1} {n}^{6 + 4} \\ = 54 {m}^{19} {n}^{10} [/tex]
Answer:
[tex]54 {m}^{19} {n}^{10} [/tex]
Hope you could get an idea from here.
Doubt clarification - use comment section.
Answer:
Solution given:
[tex]\bold{(3m^6n²)³.2mn⁴}[/tex]
distribute power
[tex]3³m^{6*3}n^{2*3}.2mn⁴[/tex]
[tex]27m^{18}n^6.2mn⁴[/tex]
multiply like terms and add or subtract power in multiplication
[tex]27*2.m^{18+1}n^{6+4}[/tex]
[tex]\large{\bold{54m^{18}n^{10}}}[/tex] is a required answer
22. PLEASE HELP PLEASSSSSSEEEEEEEE
Answers
Answer:
me too i need help its in my HW and exam
Step-by-step explanation:
A tree casts a shadow of 69.53 feet. A 5 feet pole casts a shadow of 8.97 feet. Find
the height of the tree.
Answers
Answer:
The height of the tree is 38.76.
Step-by-step explanation:
[tex]\frac{x}{69.53} =\frac{5}{8.97}[/tex]
x= [tex]\frac{69.53x5}{8.97}[/tex]
69.53x5= 347.65
347.65 8.97= 38.75696767
round the number (38.76)
Hope this helps
sorry if its wrong
Emily is entering a bicycle race for charity. Her mother pledges $0.20 for every 0.75 miles she bikes. If Emily bikes 24 miles, how much will her mother donate?
Answers
Answer:
4 dollars and 80 cents
Step-by-step explanation:
24 times 20 is 480 but its money so u would say $4.80.
How many 1/4 inch cubes does it take to fill a box with width 1 inches, length 3 3/4 inches and height 1 1/2inches?
Answers
Step-by-step explanation:
we need to see how many cubes fit into every dimension.
we can fit 4 cubes along the 1 in width. as 4×1/4 = 1 in.
we can fit 15 cubes along the 3 3/4 in length :
3 3/4 = 12/4 + 3/4 = 15/4
15/4 / 1/4 = 15/4 × 4/1 = 4×15 / 4×1 = 15
we can put 6 cubes on top of each other fit the height of 1 1/2 in
1 1/2 = 2/2 + 1/2 = 3/2 = 6/4
6/4 / 1/4 = ... = 6 (as above - simply 1/4 fits 6 times into 6/4).
so, we have
4 × 15 × 6 = 360
we need 360 cubes to fill the box.
6
0 0 0
TIME RE
44
Jeremiah flies an airplane for 2.7 hours at an average speed of 304.6 miles per hour. How far did Jeremiah fly?
Answers
Answer:
112.81 miles
Step-by-step explanation:
304.6 divided by 2.7
write the equation of the line that passes through the points ( 1, -1) and (0, 5)
Answers
Answer:
y=-6x+5
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(5-(-1))/(0-1)
m=(5+1)/-1
m=6/-1
m=-6
y-y1=m(x-x1)
y-(-1)=-6(x-1)
y+1=-6(x-1)
y=-6x+6-1
y=-6x+5
In a computer tape library there are two racks with 50 tapes per rack. On Monday there are 35 tapes in use, on Tuesday 60, and on Wednesday 25. What fraction on the average is in use for the 3 days
Answers
Based on the number of tapes used on those days and the number of tapes in the rack, the fraction on the average used was 2/5
The average tapes used in those 3 days was:
= (35 + 60 + 25) / 3
= 120 / 3
= 40 tapes
The total number of tapes that can be used are:
= 50 + 50 per rack
= 100 tapes
The fraction of the average is:
= 40 / 100
In the lowest term this is:
= 2 / 5
In conclusion, the fraction is 2/5
Find out more about fractions at https://brainly.com/question/233783.
Of 92 adults selected randomly from one town, 61 have health insurance. Find a 90% confidence interval for the true proportion of all adults in the town who have health insurance. Group of answer choices 0.582 < p < 0.744 0.548 < p < 0.778 0.536 < p < 0.790 0.566 < p < 0.760
Answers
A 90% confidence interval for the true proportion of all adults in the town who have health insurance is 0.582 < p < 0.744
The formula for calculating the confidence interval is expressed as;
[tex]CI=p \pm z \cdot\sqrt{\frac{P(1-p)}{n} }[/tex]
p is the proportion = 61/92 = 0.66n is the sample size = 92z is the z-score at 90% = 1.645Substitute the given parameters into the formula to have:
[tex]CI=0.66 \pm 1.645 \cdot\sqrt{\frac{0.66(1-0.66)}{92} }\\CI=0.66 \pm 1.645 \cdot\sqrt{\frac{0.66(0.34)}{92} }\\CI =0.66\pm 1.645(0.0495)\\CI=0.66 \pm 0.0814\\CI = (0.582, 0.744)[/tex]
Hence a 90% confidence interval for the true proportion of all adults in the town who have health insurance is 0.582 < p < 0.744
Learn more on confidence interval here: https://brainly.com/question/15712887
Which expression is equivalent to 3(2t + 6) – 4t?
A. 8t
B. 20t
C. 2t +6
D. 2t +18
HELP PLS
Answers
Answer:
b part 20 t or i think c part 2t +6
6 miles is approximately equal to 9 km. How many km are equal to 54
miles? How many miles are equal to 12 km?
Answers
Answer:
54mile equal to 81km
8mile equal to 12km
Find the product of ( - 6 + 3i) and its conjugate.
product =
Submit Question
Answers
Answer:
45Step-by-step explanation:
The conjugate of the given is:
( - 6 - 3i)Find their product:
(- 6 + 3i)( - 6 - 3i) = (-6)² - (3i)² = 36 - 9i² = 36 - 9(- 1) = 36 + 9 = 45Which of the following points lies on the line 2x+3y=5?
A. (2,3)
B. (2,1)
C. (-2,3)
D. (-2,0)
Answers
Answer:
B(2,1). And C(-2,3)
Step-by-step explanation:
Tbh, you can just plug the numbers into the original equation :2x+3y=5
A.2x2+3x3=13 ≠5
B.2x2+3x1=5=5
C.-2x2+3x3=5=5
D.-2x2+3x0=-4≠5
So the answer is B and C lies on the line
Part B: If Andrew drives 6 more hours at the same rate, what is the total number of miles traveled for the trip?
Answers
The functions r and s are defined as follows.
r(x) = - 2x-1
s(x)=x2-1
=
Find the value of r(s (3)).
Answers
Answer:
r o s(3)=?
s(x)= x²-1
x=3
s(3)= 3²-1
s(3)= 9-1
s(3)=8
r(8)
r(x)= -2x-1
x=8
r(8)= -16-1
r(8)= -17
r(s(3))= -17
Mario has save $200 towards the cost of buying a $1000 computer in the weeks to come he passes seven additional $30 per week create an expression that represents the amount of money Mario has saved after W weeks
Answers
Answer:
30w+200=1000
Step-by-step explanation:
1,256 balls divided by 13 games. About how many balls should each game get? Estimate answers are:
A. About 80
B. About 100
Those are the choices. 80 is not enough and 100 is too many. 90 or 96R8 not there. Ugh.
Answers
If you round 1256 to 1300 and then divide it by 13 you get about 100
heleppppppppppppp
plssssssssssssssss
Answers
Answer:
21
Step-by-step explanation:
Answer:
(3,3)
Step-by-step explanation:
Point B is the only point that inside the rectangle alone. Point A is not found in any shape and points C and D are inside the oval. coordinates are labeled (x,y). The coordinates of point B are (3,3)
I understand if this a little difficult to understand and i sincerely apologize for that..
1
If f(x) = -3x-2, find f(-7)
Answers
Answer:
19
Step-by-step explanation:
f(x)= -3x-2
f(-7)= -3(-7)-2
= 21 - 2
= 19
hope this helps! :D
There were 560 people at a play. The admission price was $2 for
adults and $1 for children. The admission receipts were $860.
How many adults and how many children attended?
Answers
Answer:
• For this one we need to split this problem into two equations:
• a (adults) + c (children) = 560
• 2a + c = $860
• Then we substitute 560 - a for c in the second equation.
2a + 560 - a = 8602a + 560 = 8602a = 5302a = 265• Then we plug this into the first equation:
265 + c = 560c = 295Step-by-step explanation:
I hope this helps you !!Find the value of x in the figure below
Answers
Answer:
37
Step-by-step explanation:
Both the x and the 53 add up to 90 so you subtract 53 from 90 and you get 37