Answer:
a) The standard deviation of this sampling distribution is 2.07.
b) The missing number is 4.14.
c) The 95% confidence interval for the population mean score μ based on this one sample is between 267.86 and 276.14.
Step-by-step explanation:
To solve this question, we need to understand the Empirical Rule and the Central Limit Theorem.
Empirical Rule:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
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.
In this question:
[tex]\mu = 272, n = 840, \sigma = 60[/tex]
(a) If we take many samples, the sample mean x⎯⎯⎯ varies from sample to sample according to a Normal distribution with mean equal to the unknown mean score μ in the population. What is the standard deviation of this sampling distribution?
Using the Central Limit Theorem:
[tex]s = \frac{\sigma}{\sqrt{n}} = \frac{60}{\sqrt{840}} = 2.07[/tex]
The standard deviation of this sampling distribution is 2.07.
(b) According to the 95 part of the 68-95-99.7 rule, 95% of all values of x⎯⎯⎯ fall within _______ on either side of the unknown mean μ. What is the missing number?
Within 2 standard deviations of the mean.
So, 2*2.07 = 4.14
The missing number is 4.14.
(c) What is the 95% confidence interval for the population mean score μ based on this one sample?
Within 4.14 of the mean
272 - 4.14 = 267.86
272 + 4.14 = 276.14
The 95% confidence interval for the population mean score μ based on this one sample is between 267.86 and 276.14.
Evaluate if c=4 and a=2
2-C+a
Answer:
0
Step-by-step explanation:
2 - c(4) is -2. -2 + a(2) is 0.
Hope it helps!
Help, quick! Worth 100 points
Equation 1
x-3=2-4x
Which of these have the same answer as equation 1?
A.) 2x-6=4-8x
B.) x-5=-4x
C.) 2(1-2x)=x-3
D.) -3=2-5x
Answer:
the answer is (C) 2(1-2x)=x-3
PLEASE HELP GIVING BRAINLIEST
f(n) = n2 + 4n
g(n) = - 2n - 2
Find f(n) + g(n)
Answer:
(g x h)(n) = -3n(n^2+2n+4) + 2(n^2+2n+4)
(g x h)(n) = -3n^3-4n^2 -8n + 8
(g x h)(1) = -3n^3-4n^2 -8n + 8 = -3 -4 -8 + 8 = -7
Step-by-step explanation:
Answer:
1. n = 0
n = f -4
2. n = - 2/g+2
3. fn+gn
Step-by-step explanation:
Please help w my math homework giving a 100 points
Answer:
It is only 5 point not 100,she cappin
Step-by-step explanation:
Help plssssss it’s an emergency
Answer:
All I know is that the -3 should be there without the 1/3 because that makes no sense to me. And...
Step-by-step explanation:
3x+8=-4
Subtract 8 from both sides.
3x+8−8=−4−8
3x=−12
Step 2: Divide both sides by 3.
3x=−12
3 3
x=−4
Answer: Tyler's work is incorrect because when subtracting 8 from both sides of the equation, he didn't subtract it from -4. If he subtracted 8 from -4, it would've been 3x=-12.
The correct answer is x = -4
Step-by-step explanation:
you get x = -4 by subtracting 8 from each side of the equation, resulting in 3x = -12
then you divide both sides by 3, leaving you with x = -4
Mark got 18 out of 25 questions correct on his science test. What percent of the questions did he get incorrect
Answer:
28%. mark got 28% WRONG
Step-by-step explanation:
another way to write 18/25 is 18 divided by 25. 18/25=0.72. 0.72 as a percentage is 72%. You are asking what percent he got wrong. 100%-72%=28%. Mark got 28% wrong/
Submit the worksheet with your constructions to your teacher to be graded. Click on the SAVE button to indicate that the assignment is complete.
Answer:
mom?
Step-by-step explanation:
Subtract -b + 3 from -11b -4 a. 10b+7 b. -12 - 1 c. 10b - 7 d. -10b - 7
Answer:
d. -10b-7
Step-by-step explanation:
Pls help I’m failing
Answer:
-7
Step-by-step explanation:
you divide both sides by -2 and 14/-2 is equal to -7
A bakery sold a total of 120 cupcakes in a day, and 45% of them were chocolate flavored. How many of the cupcakes sold that day were chocolate flavored?
Answer:
66 are chocolate. 120x1.45 66
The number of cupcakes sold that day was chocolate flavored will be 54.
What is the percentage?The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol '%' is used to symbolize it.
A bakery sold a total of 120 cupcakes in a day, and 45% of them were chocolate flavored.
Then the number of cupcakes sold that day were chocolate flavored will be
Let x be the number of the cupcakes sold that day that was chocolate flavored.
x = 45% of 120
x = 0.45 × 120
x = 54
Thus, the number of cupcakes sold that day was chocolate flavored will be 54.
More about the percentage link is given below.
https://brainly.com/question/8011401
#SPJ2
Evaluate the expression 4x+3-x for
x=8
PLEASE HELP ME!
Answer:
x + 3 =8 x 4 =32 so your answer is 32 sorry for he wait
Step-by-step explanation:
x =5
Write an explicit formula for the nth term or the sequence 8,-24, 72
Answer:
[tex]T_n =-\frac{8}{3} (-3)^{n}[/tex]
Step-by-step explanation:
Given
[tex]Sequence: 8, -24, 72[/tex]
Required
Determine the n term
The above sequence is geometric. So, we calculate the common ratio first:
[tex]r = \frac{T_2}{T_1}[/tex]
[tex]r = \frac{-24}{8}[/tex]
[tex]r = -3[/tex]
The equation is then calculated using:
[tex]T_n = ar^{n-1}[/tex]
Where
[tex]a = T_1 = 8[/tex]
and
[tex]r = -3[/tex]
The equation becomes:
[tex]T_n =8 * (-3)^{n-1}[/tex]
Apply law of indices:
[tex]T_n =8 * (-3)^{n} * (-3)^{-1}[/tex]
[tex]T_n =8 * (-3)^{n} * \frac{1}{-3}[/tex]
[tex]T_n =-8 * (-3)^{n} * \frac{1}{3}[/tex]
[tex]T_n =-\frac{8}{3} * (-3)^{n}[/tex]
[tex]T_n =-\frac{8}{3} (-3)^{n}[/tex]
Monica paid sales tax of $105 when she bought a new TV. If the sales tax is 5%, what was the cost of the TV?
Answer:
$31.5
Step-by-step explanation:
X * 5% = $1.50
X = $1.50 / 5%
Or by using simple rule of three:
If 5% is $1.50
Then 100% is X
So you obtain = $30
Now you just need to sum The net prices and the taxes
Net + tax = Total Charge
$30 + $1.5 = $31.5
1. How do you find the slope in a graph?
Someone help solve ill gift you nitro :)
Find the solution to the equation. URGENT
Answer:
x + 6 + x + 6 + x + 6 + x + 6 + x + 6 x + 6 + x + 6 + x + 6 = 120
aka 8(6 + x) = 120
48 + 8x = 120
you want to get 8x on one side so you will subtract 48 on both sides - whatever you do to obe side you must do on the other side.
8x = 72
now you want the x by its self so to undo multiplication you need to divide, and divide on both sides.
x = 9
Solution: x = 9
THIS IS A BREAK QUESTION
what is your favorite school subject
Answer:
Art
Step-by-step explanation:
...................
Answer:
Music
Step-by-step explanation:
Have a good rest of your day!
Which point is a reflection of (-4,-3) across the y-axis?
O (3, 4)
O (4, -3)
O (-3,-4)
O (4,3)
Answer:
The point after the reflection of (-4,-3) across the y-axis is:
(4, -3)Hence, option B is correct.
Step-by-step explanation:
When a point P(x, y) is reflected across the y-axis, we reverse the sign of the x-coordinate while the y-coordinate remains the same.
Thus,
The rule to reflect a point across the y-axis is:
P(x, y) → P'(-x, y)
In our case, we are given the point (-4, -3)
Let say the point is A(-4, -3)
Thus, using the rule to reflect a point across the y-axis is:
P(x, y) → P'(-x, y)
A(-4, -3) → A'(-(-4), -3) → A'(4, -3)
Therefore, the point after the reflection of (-4,-3) across the y-axis is:
(4, -3)Hence, option B is correct.
Write the slope intercept form of the equation of the line through the given point with the given slope.
through: (1.-3), slope = -1
Answer:
y=-x-2
Step-by-step explanation:
y-y1=m(x-x1)
y-(-3)=-1(x-1)
y+3=-1(x-1)
y=-x+1-3
y=-x-2
SOMEONE PLEASE HELP QUESTION NUMBER 5
Answer:
Angle 7 and 9 = 49 degrees.
Angle 8 and 10 = 41 degrees
The sum of two consecutive integers is at least 14.
What is the least possible pair of integers?
A. 6 and 7
B. 4 and 5
C. 8 and 9
D. 7 and 8
Answer:
its 7 and 8
Step-by-step explanation:
chapter 13 medical math assignment sheet cengage learning a dental laboratory technician (DLT) earns $14 per hour when she works days and $18 per hour when she works nights. One month she works six 4-hour days, three 8-hour days, three 10-hour days, five 6-hour nights, and four 8-hour nights. What is her total pay for the month
Answer:
$2,208
Step-by-step explanation:
In order to calculate her total pay for the month we simply need to use the hours provided in the question, multiply each amount of hours by they pay rate for that day/night. Finally, we add all of the products together to get the final pay for the month.
6 * (4*14) = 336
3 * (8 * 14) = 336
3 * (10 * 14) = 420
5 * (6 * 18) = 540
4 * (8 * 18) = 576
336 + 336 + 420 + 540 + 576 = $2,208
Finally, we can see that her total pay for the month is $2,208
What is the shape of the cross section formed by a plane slicing parallel to the base?
A) rectangle
B) square
C)circle
D) triangle
Answer:
triangle
Step-by-step explanation:
Answer:
triangle
Step-by-step explanation:
On a coordinate plane, 3 parallelograms are shown. Parallelogram A B C D has points (3, 5), (6, 5), (4, 1), (1, 1). Parallelogram A prime B prime C prime D prime has points (3, negative 5), (6, negative 5), (4, negative 1), (1, negative 1). Parallelogram A double-prime B double-prime C double-prime D double-prime has points (negative 3, negative 4), (0, negative 4), (negative 2, 0), (negative 4, 0). Which rule describes the composition of transformations that maps pre-image ABCD to final image A"B"C"D"? Reflection across the x-axis composition translation of negative 6 units x, 1 unit y. Translation of negative 6 units x, 1 unit y composition reflection across the x-axis. 90 degree rotation about point 0 composition translation of negative 6 units x, 1 unit y. Translation of negative 6 units x, 1 unit y composition 90 degree rotation about point 0.
please helpppppp ;( ILL MARK BRAINLIEST IF CORRECT
Answer:
It would be a reflection across the x-axis, followed by a composition translation of -6 units x, and 1 unit y.
Step-by-step explanation:
If you were to graph each shape and follow this procedure, you will go from parallelogram ABCD to parallelogram A''B''C''D''.
Determine which of the following words best describes the underlined word(s) in the context.
The President of a mobile phone manufacturer wants to know what color mobile phone users prefer. The company sells mobile phones throughout the world. There are 5.16 billion unique mobile phone users in the world. A Statistician for the manufacturer conducts a random sample of 1,000 mobile phone users throughout the world and from the sample determines that 23.6% prefer white and 34.6% black.
variable, population, statistic, sample, data, parameter
Answer:
Population - All 5.16 billion mobile phone users
Sample - subset of 1000 chosen from 5.16 billion
Variable - white and black mobile preference
Parameter - statistical characteristics of the population
Statistic - statistical characteristic of the sample ; 23.6% white preference ; 34.6 black preference
Data - facts and figures gathered for the study
Step-by-step explanation:
The population is the total observations who fit into a certain area of interest.
Sample refers to subset of the population which is meant to be representative of the larger population.
Variable refer to groups of characteristics with relates to observations within a dataset.
Parameter - statistical characteristics of the population
Statistic - statistical characteristic of the sample
Data - facts and figures gathered for the study
Find the Greatest common factor
42,60
Answer:
6
Step-by-step explanation:
Greatest common factor (GCF) of 42 and 60 is 6.
As the numbers get larger, or you want to compare multiple numbers at the same time to find the GCF, you can see how listing out all of the factors would become too much. To fix this, you can use prime factors.
List out all of the prime factors for each number:
Prime Factors for 42: 2, 3, and 7
Prime Factors for 60: 2, 2, 3, and 5
Now that we have the list of prime factors, we need to find any which are common for each number.
Looking at the occurences of common prime factors in 42 and 60 we can see that the commonly occuring prime factors are 2 and 3.
To calculate the prime factor, we multiply these numbers together:
GCF = 2 x 3 = 6
(hope this helps can i plz have brainlist :D hehe)
PLEASE HELP!! 30 POINTS
What is the length of leg s of the triangle below?
45°
132
s
45°
4
What is the measure of Angle E?
Answer:
B)
Step-by-step explanation:
1) the sum of angles of triangle is 180, then
180=25+33+E;
2) the measure of the angle E is:
E=180-25-33=122°
3) correct answer is B) 122°
kiara is paid 76.95 twice a month.how much money does she make in a year
Answer:
1,846.8
Step-by-step explanation:
76.95x2= 153.9
153.9x12= 1,846.8
Suppose you are hired by the STAR Lab to analyze vehicle arrivals at the right lane of the Evergreen Point Bridge on Westbound SR-520 for the period from 12:00am to 4:00am in a weekday. It is known that vehicle arrivals follow a Poisson process at this location and time period. There is a single-loop detector embedded on this lane at the east end of the bridge. Since you do not want to go to the bridge to count vehicles at this time period, you decided to use the loop detector data for the analysis. Of the 720 20-second intervals (the loop detection system stores data every 20 seconds), 508 intervals were identified to have at least one vehicle detected. Assume the loop detector is free of error. Please estimate the vehicle arrival rate (vehicles per second) for this lane. With the estimated arrival rate, please calculate the probability of having three or more vehicles detected in a 20-second interval and the probability of having a headway shorter than 10 seconds. [15 points]
Answer:
0.126
Step-by-step explanation:
Given :
Total time interval = 720
Number of interval in which one vehicle is detected =508
Proportion of atleast one detected vehicle :
508 / 720 = 0.7056
The mean arrival rate per second :
P(x ≥ 3) = 1 - P(x ≤ 3)
P(x ≥ 3) =1 - [p(x =0) + p(x = 1) + p(x =2) + p(x = 3)]
P(x ≥ 3) = 1 - 0.8745
P(x ≥ 3) = 0.1255
P(x ≥ 3) = 0.126