Asked by kiki
Mrs. Jones Algebra 2 class scored very well on yesterday’s quiz. With one exception, everyone received an A. Within how many standard deviations from the mean do all the quiz grades fall? 91, 92, 94, 88, 96, 99, 91, 93, 94, 97, 95, 97
A. 1
B. 2
C. 3
D. 4
A. 1
B. 2
C. 3
D. 4
Answers
Answered by
Bot
We need to calculate the mean and standard deviation of the quiz grades to determine the answer. Using a calculator, we find that the mean is 94.1667 and the standard deviation is 3.106.
To determine how many standard deviations from the mean all the grades fall within, we need to calculate the difference between each grade and the mean, divide that by the standard deviation, and look for the largest absolute value.
The largest absolute value is 2.402, which is less than 3. Therefore, all the quiz grades fall within 3 standard deviations from the mean.
Answer: C. 3
To determine how many standard deviations from the mean all the grades fall within, we need to calculate the difference between each grade and the mean, divide that by the standard deviation, and look for the largest absolute value.
The largest absolute value is 2.402, which is less than 3. Therefore, all the quiz grades fall within 3 standard deviations from the mean.
Answer: C. 3
Answered by
Bot
I apologize for the error. Upon recalculation, the mean is indeed 94.1667 and the standard deviation is 3.106.
To determine how many standard deviations from the mean all the grades fall within, we need to calculate the difference between each grade and the mean, divide that by the standard deviation, and look for the largest absolute value.
The largest absolute value is 2.365, which is less than 2. Therefore, all the quiz grades fall within 2 standard deviations from the mean.
The answer is B. 2.
To determine how many standard deviations from the mean all the grades fall within, we need to calculate the difference between each grade and the mean, divide that by the standard deviation, and look for the largest absolute value.
The largest absolute value is 2.365, which is less than 2. Therefore, all the quiz grades fall within 2 standard deviations from the mean.
The answer is B. 2.
Answered by
Bot
The binomial theorem states that the expansion of the binomial expression (a+b)^n is:
(a+b)^n = C(n,0)a^n b^0 + C(n,1)a^(n-1) b^1 + C(n,2)a^(n-2) b^2 + ... + C(n,n-1)a^1 b^(n-1) + C(n,n)a^0 b^n
where C(n,k) = n! / (k!(n-k)!) represents the binomial coefficient.
Applying this to the expression (d-5)^6, we have:
(d-5)^6 = C(6,0)d^6 (-5)^0 + C(6,1)d^5 (-5)^1 + C(6,2)d^4 (-5)^2 + ... + C(6,4)d^2 (-5)^4 + C(6,5)d^1 (-5)^5 + C(6,6)d^0 (-5)^6
Simplifying each term using the binomial coefficient formula, we get:
(d-5)^6 = d^6 - 30d^5 + 375d^4 - 2500d^3 + 9375d^2 - 15625d + 15625
Therefore, the binomial expansion of (d-5)^6 is:
d^6 - 30d^5 + 375d^4 - 2500d^3 + 9375d^2 - 15625d + 15625
(a+b)^n = C(n,0)a^n b^0 + C(n,1)a^(n-1) b^1 + C(n,2)a^(n-2) b^2 + ... + C(n,n-1)a^1 b^(n-1) + C(n,n)a^0 b^n
where C(n,k) = n! / (k!(n-k)!) represents the binomial coefficient.
Applying this to the expression (d-5)^6, we have:
(d-5)^6 = C(6,0)d^6 (-5)^0 + C(6,1)d^5 (-5)^1 + C(6,2)d^4 (-5)^2 + ... + C(6,4)d^2 (-5)^4 + C(6,5)d^1 (-5)^5 + C(6,6)d^0 (-5)^6
Simplifying each term using the binomial coefficient formula, we get:
(d-5)^6 = d^6 - 30d^5 + 375d^4 - 2500d^3 + 9375d^2 - 15625d + 15625
Therefore, the binomial expansion of (d-5)^6 is:
d^6 - 30d^5 + 375d^4 - 2500d^3 + 9375d^2 - 15625d + 15625
Answered by
Bot
To find the 30th percentile, we need to arrange the data from smallest to largest:
100, 100, 105, 113, 129, 132, 146, 152, 176, 200
The 30th percentile corresponds to the data value that has 30% of the data below it and 70% above it. To find the position of the 30th percentile value, we can use the formula:
Position = (percentile/100) x (n+1)
where n is the number of data values.
For the 30th percentile, we have:
Position = (30/100) x (10+1) = 3.3
Since 3.3 is not a whole number, we need to interpolate between the 3rd and 4th values in the ordered data set.
30th percentile = 100 + 0.3 x (105-100) = 100 + 0.3 x 5 = 101.5
Therefore, the 30th percentile is 101.5.
To find the 90th percentile, we again arrange the data from smallest to largest:
100, 100, 105, 113, 129, 132, 146, 152, 176, 200
The 90th percentile corresponds to the data value that has 90% of the data below it and 10% above it. Using the same formula as before, we have:
Position = (90/100) x (10+1) = 9.9
Since 9.9 is not a whole number, we need to interpolate between the 9th and 10th values in the ordered data set.
90th percentile = 176 + 0.9 x (200-176) = 176 + 0.9 x 24 = 198.6
Therefore, the 90th percentile is 198.6.
100, 100, 105, 113, 129, 132, 146, 152, 176, 200
The 30th percentile corresponds to the data value that has 30% of the data below it and 70% above it. To find the position of the 30th percentile value, we can use the formula:
Position = (percentile/100) x (n+1)
where n is the number of data values.
For the 30th percentile, we have:
Position = (30/100) x (10+1) = 3.3
Since 3.3 is not a whole number, we need to interpolate between the 3rd and 4th values in the ordered data set.
30th percentile = 100 + 0.3 x (105-100) = 100 + 0.3 x 5 = 101.5
Therefore, the 30th percentile is 101.5.
To find the 90th percentile, we again arrange the data from smallest to largest:
100, 100, 105, 113, 129, 132, 146, 152, 176, 200
The 90th percentile corresponds to the data value that has 90% of the data below it and 10% above it. Using the same formula as before, we have:
Position = (90/100) x (10+1) = 9.9
Since 9.9 is not a whole number, we need to interpolate between the 9th and 10th values in the ordered data set.
90th percentile = 176 + 0.9 x (200-176) = 176 + 0.9 x 24 = 198.6
Therefore, the 90th percentile is 198.6.
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