A random sample of size n = 50 is taken from a population with mean μ = −9.5 and standard deviation σ = 2. Use Table 1.
a. Calculate the expected value and the standard error for the sampling distribution of the sample mean.(Negative values should be indicated by a minus sign. Round "expected value" to 1 decimal place and "standard deviation" to 4 decimal places.)
Expected value Standard error b. What is the probability that the sample mean is less than −10? (Round intermediate calculations to 4 decimal places, "z" value to 2 decimal places, and final answer to 4 decimal places.)
Probability c. What is the probability that the sample mean falls between −10 and −9? (Round intermediate calculations to 4 decimal places, "z" value to 2 decimal places, and final answer to 4 decimal places.)
Probability
Answers
a) The expected value of the sampling distribution is -9.5, and the standard error is approximately 0.2828.
b) The probability that the sample mean is less than -10 is approximately 0.0384, or 3.84%.
c) The probability that the sample mean falls between -10 and -9 is approximately 0.9232, or 92.32%.
a. Calculating the Expected Value and Standard Error:
The expected value (also known as the mean) of the sampling distribution of the sample mean is equal to the population mean (μ). In this case, the population mean is given as μ = -9.5. Therefore, the expected value of the sampling distribution is also -9.5.
The standard error (SE) represents the standard deviation of the sampling distribution. It measures the average deviation of the sample means from the expected value. The formula to calculate the standard error is:
SE = σ / √(n)
where σ is the population standard deviation and n is the sample size.
Given that the population standard deviation is σ = 2 and the sample size is n = 50, we can substitute these values into the formula to find the standard error:
SE = 2 / √(50) ≈ 0.2828
b. Probability that the Sample Mean is Less than -10:
To find the probability that the sample mean is less than -10, we need to use the sampling distribution and Table 1. Since the sampling distribution of the sample mean is approximately normally distributed (central limit theorem), we can use Table 1 to find the corresponding probability.
First, we need to calculate the z-score for the value -10 using the formula:
z = (x - μ) / SE
where x is the value of interest, μ is the expected value, and SE is the standard error.
Substituting the values, we get:
z = (-10 - (-9.5)) / 0.2828 ≈ -1.77
Next, we look up the corresponding probability in Table 1 for the z-score of -1.77. The table provides the area under the standard normal distribution curve to the left of a given z-score. In this case, we want the probability to the left of -1.77. Looking up -1.77 in Table 1, we find that the corresponding probability is approximately 0.0384.
c. Probability that the Sample Mean Falls between -10 and -9:
To find the probability that the sample mean falls between -10 and -9, we need to use the sampling distribution and Table 1.
First, we calculate the z-scores for the values -10 and -9 using the formula mentioned earlier:
z₁ = (-10 - (-9.5)) / 0.2828 ≈ -1.77
z₂ = (-9 - (-9.5)) / 0.2828 ≈ 1.77
Next, we find the corresponding probabilities for each z-score using Table 1. The table provides the area under the standard normal distribution curve to the left of a given z-score. In this case, we want the probability between -1.77 and 1.77.
From Table 1, we find that the probability to the left of -1.77 is approximately 0.0384. Similarly, the probability to the left of 1.77 is also approximately 0.9616.
To find the probability between -1.77 and 1.77, we subtract the probability to the left of -1.77 from the probability to the left of 1.77:
0.9616 - 0.0384 = 0.9232
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Related Questions
What happens when the scale factor is less than 1? What happens when the scale factor is greater than 1?
Answers
Answer:
When the absolute value of the scale factor is lower than 1, it decreases the size of the shape.
When the absolute value of the scale factor is greater than 1, the shape will increase in size.
How to Remember it:
Think if the number is a fraction, the shape will be a fraction of the size.
A six sided die is rolled and the spinner on the right is spun.What is the probabiliy of rolling a 6 and spining a vowel
Answers
Kindly note that the spinner diagram. Wasn't given and the spinner used was just hypothetical.
Answer:
1 /18
Step-by-step explanation:
Sample space for spinner = (a, b, c, d, e, F, G, h, I) = 9
Total possible outcomes = sampme space
Vowels in spinner = (a, e, I)
Number of vowels = required outcome = 3
P(spinning a vowel) = required outcome / Total possible outcomes
P(spinning a vowel) = 3 / 9 = 1/3
For a six sided dice ;
Required outcome = (6) = 1
Total possible outcomes = (1,2,3,4,5,6) = 6
P(rolling a six) = 1/6
P(rolling a 6 and spinning a vowel) = 1/3 * 1/6 = 1/18
Suppose we take a survey and use the sample proportion to calculate a confidence interval. Which level of confidence gives the confidence interval with the largest margin of error
Answers
Answer:
See below
Step-by-step explanation:
I do not see any options, but it is important to note that the bigger the level of confidence, the larger the margin of error will be.
Referring to the figure, find the measure of arc MLK
Answers
Measure of arc MLK is 270°
Explanation:Angle MKL = 135 degrees
We are looking for the measure of the arc MLK
The diagram shows an angle formed by a chord (MK) and tangent
The relationship between angle formed by a chord and tangent:
\(Inscribed\text{ angle = }\frac{1}{2}\text{ m of arc MLK}\)Measure of arc MLK:
\(\begin{gathered} \text{Measure of arc MLK = 2(inscribed angle)} \\ \\ In\text{scribed angle = 135}\degree\text{ } \\ \text{Measure of arc MLK = 2(135)} \\ \text{Measure of arc MLK = }270\degree \end{gathered}\)
Each histogram represents a set of data with a median of 29.5. Which set of data most likely has a mean that is closest to 29.5?
A graph shows the horizontal axis numbered 9 to 48. The vertical axis is numbered 1 to 5. The graph shows an upward trend from 1 to 33 then a downward trend from 33 to 45.
A graph shows the horizontal axis numbered 15 to 48. The vertical axis is numbered 1 to 5. The graph shows an upward trend from 1 to 30 then a downward trend from 30 to 45.
A graph shows the horizontal axis numbered 12 to 56. The vertical axis is numbered 2 to 8. The graph shows an upward trend from 1 to 32 then a downward trend from 32 to 56.
A graph shows the horizontal axis numbered 15 to 54. The vertical axis is numbered 1 to 5. The graph shows an upward trend from 1 to 24, a downward trend from 24 to 27, an upward trend from 27 to 30, a downward trend from 30 to 39, an upward trend from 39 to 45, a downward trend from 45 to 48, then an upward trend from 48 to 51.
Answers
To determine which set of data most likely has a mean closest to 29.5, we need to analyze the shape and position of the histograms in relation to the value 29.5.
Looking at the histograms described:
The first histogram ranges from 9 to 48, and the upward trend starts from 1 and ends at 33, followed by a downward trend. This histogram suggests that there may be values lower than 29.5, which would bring the mean below 29.5.
The second histogram ranges from 15 to 48, with an upward trend from 1 to 30 and then a downward trend. Similar to the first histogram, it suggests the possibility of values lower than 29.5, indicating a mean below 29.5.
The third histogram ranges from 12 to 56, and the upward trend starts from 1 and ends at 32, followed by a downward trend. This histogram covers a wider range but still suggests the possibility of values below 29.5, indicating a mean below 29.5.
The fourth histogram ranges from 15 to 54 and exhibits multiple trends. While it has fluctuations, it covers a wider range and includes both upward and downward trends. This histogram suggests the possibility of values above and below 29.5, potentially resulting in a mean closer to 29.5.
Based on the descriptions, the fourth histogram, with its more varied trends and wider range, is most likely to have a mean closest to 29.5.
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write an equation that represents the data in the table:
x - 5, 10, 15, 20
y - 17, 22, 27, 32
Answers
I
7. The total cost to rent a truck is $100 and $0.20 per km.
a. Determine an algebraic model for the relationship between total cost and distance driven. Use C to
represent total cost (S) to rent the truck and d to represent distance driven (km).
Answers
Answer:
C= 100+ d*0.2
Step-by-step explanation:
Give data
Cost of rental = $100
Cost per km= $0.2
Total cost= C
Distance= d
Let us model the expression
Hence the expression is given as
C= 100+ d*0.2
Parking lots A and B each charge a set fee for parking plus an hourly rate.
Hours Parked48Lot A Cost ($)19.00/33.00
Lot B Cost ($)20.00/32.00
How many more dollars does it cost per hour to park in Lot A than in Lot B? Give the answer as a decimal showing dollars and cents.
Answers
Answer:
$0.5
Step-by-step explanation:
Given :
Hours ___Lot A Cost ($) ___ Lot B Cost ($) 4____________19.00 _____ 20.00
8 ___________ 33.00 ______ 32.00
Using the equation :
y = mx + C
m = slope = Hourly charge
C = intercept = set park fee
m = y2 - y1 / x2 - x1
For LotA:
m1 = (33 - 19) / (8 - 4)
m1 = 14 / 4
m1 = 3.5
For LotB:
m2 = (32 - 20) / (8 - 4)
m2 = 12 / 4
m2 = 3
Since, m is the hourly cost :
Difference = m1 - m2
= 3.5 - 3
= $0. 5
PLS HELP ASAP THANKS ILL GIVE BRAINLKEST PLS THANKS PLS
Answers
Answer:
A
Step-by-step explanation:
Your mouse is in the way but that’s what I can tell by looking at the graph
find the sum
(2x+6)+(4x-12)
HELp
Answers
Answer:
6x - 6
Step-by-step explanation:
(2x + 6) + (4x - 12) ← remove parenthesis
= 2x + 6 + 4x - 12 ← collect like terms
= (2x + 4x) + (6 - 12)
= 6x + (- 6)
= 6x - 6
Jason solved for the quotient of 133.5 ÷ 5.
5 StartLongDivisionSymbol 133.5 EndLongDivisionSymbol minus 10 = 33. 33 minus 30 = 35. 35 minus 35 = a remainder of 0 and quotient of 267. Answer: 133.5 divided by 5 = 267.
What was Jason’s error?
Jason did not multiply correctly.
Jason should have moved the decimal before dividing.
Jason did not put the correct decimal in the quotient.
Jason did not make an error.
Answers
Answer:
Hi there! The answer is C
Step-by-step explanation:
I did it on edge 2020! have a nice day!
Answer:
yo
Step-by-step explanation:
C on edgenuinity
At the sewing store, Linda bought a bag of mixed buttons. The bag included 70 buttons, of which 30% were large. How many large buttons did Linda get?
Answers
Answer:
21
Step-by-step explanation:
6/27 = 4/x
Find the answer, hint- 6x = 27x4
then divide 6 by 27x4
Answers
Answer: 18
Step-by-step explanation
Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 27x, the least common multiple of 27,x.
x × 6=27 × 4
Multiply 27 and 4 to get 108.
x × 6=108
Divide both sides by 6.
x= 108/6
Divide 108 by 6 to get 18.
x=18
A diver dove from a board that was 6 3/4 feet above the water's surface, and descended until he was 8 1/3 feet below the water's surface. What was the total distance that the diver desceded?
Answers
Answer:
15 1/12 feet
Step-by-step explanation:
Well if he descended 8 1/3 feet below the water, that means he must've went from board to water which is 6 3/4 feet then down 8 1/3 feet
6 3/4 + 8 1/3
= 6 9/12 + 8 4/12
=15 1/12 feet
In order to add
3/4 and 7/10
you need to find equivalent fractions that have the same denominators. What is a common denominator?
Answers
Answer:
a shared multiple of the denominators of several fractions
Explanation : The denominator is the number at the bottom of the fraction and when two fractions have the same number at the bottom(denominator) then they have a common denominator.
I need help please with 6, 7 and 8
Answers
6. Solution for |2x-3| = |x| are x = 1,3
7. Solution for 8 + |4v - 7| ≥ 17 is,
v ≥ 4 , v ≤ -1/2
8. Number of computer meets in the condition = 6
Average:
Average of given number is given by sum of all numbers divided by total number of numbers.
6. |2x-3| = |x|
Case I :
when x<0
|2x-3| = |x|
-(2x-3) = -x
-2x + 3 = -x
2x - x = 3
x = 3 ( Not possible as x<0 )
No solution in this case.
Case II :
when 0< x< 3/2
|2x-3| = |x|
-(2x -3) = x
-2x + 3 = x
2x +x = 3
3x = 3
x =1 (Valid solution)
Case III :
when x>3/2
|2x-3| = |x|
2x-3 = x
2x -x =3
x = 3 (Valid solution)
Thus solution for |2x-3| = |x| are x = 1,3
7.
8 + |4v - 7| ≥ 17
|4v - 7| ≥ 17 -8
|4v - 7| ≥ 9
⇒ 4v - 7 ≥ 9
4v ≥ 9+7
v ≥ 4
and,
4v - 7 ≤ - 9
4v ≤ -2
v ≤ -1/2
Thus solution for 8 + |4v - 7| ≥ 17 is,
v ≥ 4 , v ≤ -1/2
8.
We know,
Average of quantity = sum of quantity / Number of quantity
For the given question,
Sum of price of all computer = $ (890+650+ 660+450+ 725+750+370+670+650+825)
= $ 6640
and Number of computer = 10
Average price of computer = $ 6640/10
= $ 664
Absolute deviation is $100
So i can pay price between
($ 664 - $100) to ($ 664 + $100)
that is $564 to $764
Number of computer meets in this condition = 6
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A small tree was planted at a height of 17 feet. The tree has been planted for 12 months, and is now 66 feet tall. Which equation could be used to find x, the average number of feet the tree grew each month?
Answers
Answer:
12x + 17 = 66
please help me best answer gets an brainlist !!!
What values for y would complete the table provided below that would model the given equation:
y=20x+50
Question 2 options:
0, 20, 40, 60
50, 70, 90, 110
50, 100, 150, 200
20, 40, 60, 80
Answers
The answer is the range of (50, 70, 90, 110).
What is the slope of a perpendicular line to 3.2 + 4y = 9?
Answers
find ∑^200_k =99 k^3. (use table 2.)
Answers
Sum of the cubes from k = 99 to k = 200 is 380,480,499.
How to find the summation of k³ for k = 99 to 200?You can use the formula for the sum of cubes of the first n natural numbers:
∑k³ = (n(n+1)/2)²
First, we need to find the sum of the cubes from 1 to 200:
n = 200
∑k³ = (200(200+1)/2)²
∑k³ = (200(201)/2)²
∑k³ = (20100)²
∑k³ = 404010000
Next, we find the sum of cubes from 1 to 98 (we subtract one as we want to start from 99):
n = 98
∑k³ = (98(98+1)/2)²
∑k³ = (98(99)/2)²
∑k³ = (4851)²
∑k³ = 23529501
Now, subtract the sum of cubes from 1 to 98 from the sum of cubes from 1 to 200:
∑²⁰⁰_k=99 k³ = 404010000 - 23529501
∑²⁰⁰_k=99 k³ = 380480499
So, the sum of the cubes from k = 99 to k = 200 is 380,480,499.
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Which of the following equations is equivalent to 2/3 a-7 = 3?
3а - 7 = 1
3а - 7 = 3
за - 21 = 3
2a - 21 = 1
Answers
The equation which is equivalent to the given equation; 2/3 a - 7 = 1/3 as required to be determined is; 2a - 21 = 1.
Which equation is equivalent to the given equation?It follows from the task content that the correct form of the given equation is; 2/3 a - 7 = 1/3.
Therefore, in a bid to find an equivalent equation; one must multiply both sides of the equation by 3 so that we have;
2a - 21 = 1.
On this note, it can be inferred that the equation which is equivalent to the given equation is; 2a - 21 = 1
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6) A bag contains 4 red marbles, 3 green, 5 blue. Someone offers you a game : If you pick red marble you win $4, if blue loose $2, green loose $1. What is the expected value of the game
Answers
Answer:
11
Step-by-step explanation:
i just need 11 more than ill be fine
Over one weekend the fast florist makes 368 deliveries of one dozen roses. Did the fast florist deliver more then or less than 4,000 roses? Explain. That's my question ^ please help
Answers
Answer:
The florist delivered more than 4000 roses
Step-by-step explanation:
One dozen is 12 roses, so the fast florist delivered a total of 368 x 12 = 4416 roses. That is more than 4000 roses, so the answer is More than 4000 roses
what is the decimal equivalent of 0xc9?
Answers
The decimal equivalent of 0xc9 is 201.
Hexadecimals:
Hexadecimal is a number system with a base of 16, in which we use 16 distinct symbols to represent numbers. The symbols used in hexadecimal are the digits from 0 to 9 and the letters from A to F.
Hexadecimal notations are commonly used in computer programming and digital electronics because they can represent binary data more compactly than binary notation.
Here we have
0xc9
By converting each symbol as a number we can calculate as follows
Here 0x represents hexadecimal
And the value of c is 12
0xc9 = (12 × 16¹) + (9 × 16⁰)
= 192 + 9 = 201
Therefore,
The decimal equivalent of 0xc9 is 201.
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Determine whether the ratios are equivalent.
28 : 32 and 7 : 8
Answers
Answer:
They are
Step-by-step explanation:
28:32 is equal to 7/8
I need major help pls help
Answers
Answer:
No, since 832 ≠ 900, using Pythagorean theorem, the width should be 18 in
Step-by-step explanation:
It is better to type the question in the 'Question' than the fact that you need help so that we can start seeing the problem immediately.
A rectangle has 4 right angles so if l = 24 and w = 16 then you can use the pythagorean theorem to see if this is possible since
24^2 + 16^2 = 30^2 since the diagonal is the hypotenuse of the triangles formed by the diagonal in the rectangle.
576 + 256 ≠ 900, since the left side is 832 and the right side is 900
It would be more correct if the width is 18 since 576 + 18^2 = 900
Mr. Miller created a graph of the number of emergency phone calls made to 9-1-1 during one week in January. Which statement describes Mr. Miller's data?
Answers
Answer:
C or D But I think it's C, But I don't know for sure.
Step-by-step explanation: It has a total of 28 'x's so 28 x 50 = 1400
1400 divided by 7 ( Cause of the one week) is 200. if I figure out what the actual answer is I will tell you. Also be sure to read the comments.
Answer: The answer is the bottom one to the left
Step-by-step Explanation:
The sum of all the X's are 28 and if you divided that by 7 it is 4, and 4 times 50 is 200. And the highest number, which is 7, minus the smallest number which is 1 will be 6 and that times 50 is 300
Damian is buying tickets to a movie. The movie he and his friends want to see costs $ 4.85 $4.85 per ticket. Damian has $ 32.00 $32.00 total.
Answers
Answer:
What is the question?
Step-by-step explanation:
this is funny but i wish they could add the delivered sign on the bottom so it look more realistic
Answers
Answer:
yeahh and made like the profile icon on the left hahahaha
Step-by-step explanation:
Find −1/4(−8.6) . Write your answer as a decimal to the nearest hundredth.
Answers
Answer:
2.15
Step-by-step explanation:
I will assume that "−1/4(−8.6)" is telling us to multiply (-8.6) times -(1/4):
(-1/4)*(-8.6)
= (8.6/4)
= 2.15