IQ scores are normally distributed with a mean of 105 and a standard deviation of 17. Assume that many samples of size n are taken from a large population of people and the mean IQ score is computed for each sample. If the sample size is n 81, find the mean and standard deviation of the distribution of sample means.
Answers
Answer:
Mean 105
Standard deviation 1.89
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a random variable X, with mean and standard deviation
, the sample means with size n of at least 30 can be approximated to a normal distribution with mean
and standard deviation
In this problem, we have that:
If the sample size is n 81, find the mean and standard deviation of the distribution of sample means.
By the Central limit theorem
mean 105
Standard deviation
Related Questions
In the right triangle shown m
PLEASE ANSWER I NEED ITTY
Amy spent $22 on a magazine and fourerasers. If the magazine cost $6, then howmuch was each eraser?
9. Mark drinks one cup of coffee everyday. He orders a coffee from Dunkin Donuts and it costs him $3.50 everyday. He is starting to think that he might buy a Keurig and k-cups instead. The Keurig is $150 and each k-cup costs $0.50. How many cups of coffee will it take for the cost at Dunkin Donuts to be the same as having a Keurig and k-cups?
Answers
9514 1404 393
Answer:
- maximum height: 26.5 ft
- air time: 2.5 seconds
Step-by-step explanation:
I find the easiest way to answer these questions is to use a graphing calculator. It can show you the extreme values and the intercepts. The graph below shows the maximum height is 26.5 ft. The time in air is about 2.5 seconds.
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If you prefer to solve this algebraically, you can use the equation of the axis of symmetry to find the time of the maximum height:
t = -b/(2a) = -(40)/(2×-16) = 5/4
Then the maximum height is ...
h(5/4) = -16(5/4)² +40(5/4) +1.5 = -25 +50 +1.5 = 26.5 . . . feet
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Now that we know the vertex of the function, we can write it in vertex form:
h(t) = -16(t -5/4)² +26.5
Solving for the value of t that makes this zero, we get ...
0 = -16(t -5/4)² +26.5
16(t -5/4)² = 26.5
(t -5/4)² = 26.5/16 = 1.65625
Then ...
t = 1.25 +√1.65625 ≈ 2.536954
The cannon ball is in the air about 2.5 seconds.
Answers
Answer:
x = -16
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
- Left to Right
Equality Properties
Step-by-step explanation:
Step 1: Define Equation
10(1/2x + 2) - 5 = 3(x - 6) + 1
Step 2: Solve for x
- Distribute: 5x + 20 - 5 = 3x - 18 + 1
- Combine like terms: 5x + 15 = 3x - 17
- Subtract 3x on both sides: 2x + 15 = -17
- Subtract 15 on both sides: 2x = -32
- Divide 2 on both sides: x = -16
Step 3: Check
Plug in x into the original equation to verify it's a solution.
- Substitute in x: 10(1/2(-16) + 2) - 5 = 3(-16 - 6) + 1
- Multiply: 10(-8 + 2) - 5 = 3(-16 - 6) + 1
- Add/Subtract: 10(-6) - 5 = 3(-22) + 1
- Multiply: -60 - 5 = -66 + 1
- Subtract/Add: -65 = -65
Here we see that -65 does indeed equal -65.
∴ x = -16 is the solution of the equation.
bag, replaced, and another marble is drawn, what is the probability of drawing first a black marble and
then a red marble?
b. A bag contains 10 blue marbles, 9 red marbles, and 4 white marbles. If two different marbles
are drawn from the bag , what is the probability of drawing first a blue marble and then a white marble?
Answers
b. (10/23)(4/23) = .0756
Answers
Final answer:
Juan is applying basic statistical principles in a chemistry laboratory by reviewing the standard deviation of the lab measurements and repeating his measurements multiple times to find a more accurate mean. The more Juan repeats his measurements, the closer he gets to a normal distribution or an accurate mean as per the central limit theorem.
Explanation:
In this chemistry laboratory scenario, you're dealing with a situation in statistics known as repeated measurements. Essentially, you are considering the standard deviation of the lab measurements, which is a typical measure of the dispersion of a set of values. The standard deviation is denoted by σ, and it is given as 10 milligrams.
When Juan repeats the measurement 4 times and records the mean of his measurements, he's using another common measure of central tendency, the arithmetic mean.
According to the central limit theorem in statistics, the distribution of the mean of a large number of independent, identically distributed variables will be approximately normal, regardless of the underlying distribution. In this case, as Juan repeats his measurements, the mean of these measurements is likely to be more accurate (closer to the true value) than a single measurement.
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Final answer:
The standard deviation a measure of dispersion in a data set, lower values indicating data points closer to the mean of the data set, and higher values indicating a wide range of the data points. The scenario discusses the calculation of standard deviation for repeated measurements, with the standard error calculated as the original standard deviation divided by the square root of the number of measurements.
Explanation:
The subject matter of the question pertains to statistical concepts, primarily the standard deviation. In statistics, the standard deviation is a measure of the amount of variation or dispersion in a data set. A low standard deviation indicates that the data points tend to be close to the mean of the data set, while a high standard deviation indicates that the data points are spread out over a wider range.
In the scenario provided, Juan makes a measurement in a chemistry lab and the standard deviation of the students' lab measurements is 10mg. He repeats the measurement 4 times and records the mean of his 4 measurements. When you repeat a measurement multiple times and take the mean, the standard deviation of the mean tends to be smaller than the standard deviation of the individual measurements. In statistical terms, the standard deviation of the mean, also known as the standard error, is given by the original standard deviation σ divided by the square root of the number of measurements n. In this case, n is 4, so the standard error would be σ/√n = 10mg/√4 = 5mg.
Learn more about Standard Deviation here:
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Answers
A polynomial multiple by a polynomial is always a polynomial. The given statement is true.
What are polynomials?
Polynomials are those algebraic expressions that consist of variables, coefficients, and constants. The standard form of polynomials has mathematical operations such as addition, subtraction, and multiplication.
When two polynomials are multiplied by each other, then each term of the first polynomial is multiplied by each term of the second polynomial.
The result is always a polynomial, regardless of what the coefficients might be of any of the terms, including the leading coefficients.
Thus, A polynomial multiples by a polynomial is always a polynomial.
Learn more about polynomials;
Answers
Answer is provided in the image attached.
3x+3x-5= 1
6x-5=1
Whenever moving a number, the sign always changes.
6x-5+5= 1+5
6x= 1+5
6x= 6
divide both sides by 6
6x/6= 6/6
x= 1
Check solution by using the substitution method
3(1)+3(1)-5=1
3+3-5=1
6-5= 1
1=1
Answer: x=1