Answer:
Step-by-step explanation:
The 80% of students within 12 points of the mean are captured by the shaded area, which is two standard deviations away from the mean on either side.
We know that the normal distribution curve is symmetrical, so the two shaded areas have equal areas. Therefore, each shaded area has an area of 40%.
We can use the inverse normal cumulative distribution function (also known as the probit function) to find the z-scores corresponding to the 40th percentile and the 60th percentile. These z-scores are both equal to 1.28.
The z-score is defined as the number of standard deviations away from the mean:
z = (x - μ) / σ
where:
x is the observed value
μ is the mean
σ is the standard deviation
Therefore, the standard deviation is equal to:
σ = (x - μ) / z
From the sketch above, we can see that the x-value corresponding to the 40th percentile is 38 and the x-value corresponding to the 60th percentile is 62.
Substituting these values into the equation above, we can solve for the standard deviation:
σ = (62 - 50) / 1.28 = 9.375
Therefore, the standard deviation of the data so that 80% of the students are within 12 points of the mean is 9.375.
Cleverness:
To solve this problem cleverly, we can use the fact that the normal distribution curve is symmetrical. This means that we can find the standard deviation by calculating the distance between the mean and the 40th percentile, and then multiplying by 2. This is because the 40th percentile is the same distance away from the mean as the 60th percentile.
In a normal distribution with a mean of 50, if 80% of the grades are within 12 points of the mean, the standard deviation can be calculated as approximately 9.375 (option C). We obtained this result by equating the z-score that represents 80% of the data to the ratio of the score range (12 points) to the standard deviation, and solving for the standard deviation.
To determine the standard deviation given 80% of the scores are within 12 points from the mean, we need to understand the properties of a normal distribution curve. In a normal distribution, about 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and almost all (99.7%) falls within three standard deviations. Now, when we say 80% of the data falls within 12 points of the mean, we are looking at an area of the curve that is equivalent to +/- one standard deviation around the mean.
In a standard normal distribution, an area of approximately 80% correlates to a z-score of about 1.28 (using a z-table or z-score calculator). The z-score is calculated as (X - μ) / σ, where X is the score, μ is the mean and σ is the standard deviation.
In our case, we have X = ±12 (since it's 12 points above and below the mean), and μ = 0 (since we're looking at the difference from the mean). So, 1.28 = 12 / σ. Solving for σ, we get that σ = 12 / 1.28 ≈ 9.375. So the standard deviation, which provides the answer to your question, is 9.375 (option C).
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x – y = 2,342
Solve the system of equations. How many contemporary titles does Jarred have?
1,158
1,737
2,342
2,921
There are 2,921 contemporary titles does Jarred have.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
His inventory shows that he has a total of 3,500 DVDs.
He has 2,342 more contemporary titles than classic titles.
Let number of contemporary titles = x
Number of classic titles = y
The system of equations are;
⇒ x + y = 3,500
⇒ x - y = 2,342
Solve the system of equations as;
Add equation (i) and (ii) , we get;
2x = 3,500 + 2,342
2x = 5,842
Divide by 2, we get;
x = 5,842 / 2
x = 2,921
Thus, There are 2,921 contemporary titles does Jarred have.
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Answer: 336 oz
Step-by-step explanation: three 64 oz cartons = 3 * 64 = 192 oz
three 48 oz cans = 3 * 48 = 144 oz
192 + 144 = 336 oz <== total juice
Answer:
one comic book costs $5
Step-by-step explanation:
let cost of comic book = $x
let cost of vinyl = $y
according to the question:
6x = y + 3x
y = 6x - 3x
y = 3x (1)
y = $15 (2)
substituting the value of y from equation (2) into equation (1)
15 = 3x
x = 15/3 = 5
thus, cost of one comic book = $5
Answer:
5$.
Step-by-step explanation:
Let's denote the cost of one Sailor Moon comic book as x .
The cost of 6 Sailor Moon comic books is 6x.
According to the given information, the cost of a Nirvana vinyl plus 3 comic books is equal to the cost of 6 Sailor Moon comic books.
So, 15 + 3x = 6x , as the vinyl costs $15.
Now, let's solve for x :
Subtract 3x from both sides: 15 = 3x
Divide by 3: x = 5
Therefore, the cost of one Sailor Moon comic book is $5.