the mean is 146, and standard deviation is 35. A score of 251 is how many z-scores above the mean? The following figure shows the normal distribution with the proportion of the area under the normal curve containedwithin one, two, and three standard deviations of the mean. The last proportion on each side, 0.13%, depicts theremaining area under the curve. Specifically, 0.13% of the area under the standard normal distribution is locatedabove z-score values greater than the mean (P) plus three standard deviations (+30). Also, because the normaldistribution is symmetrical, 0.13% of the area under the standard normal distribution is located below z-score valuesless than the mean (µ) minus three standard deviations (-30).34.13%34.13%13.59%13.59%2.15%2.15%0.13%0.13%-30-20-10+10+20+30Use the figure to help you answer the following questions.The National Assessment of Educational Progress (NAEP) is a nationwide assessment of students' proficiency in ninesubjects: mathematics, reading, writing, science, the arts, civics, economics, geography, and U.S. history. The mainNAEP assessments are conducted annually on samples of students from grades 4, 8, and 12.the mean is 146. and standard deviation 35

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Description: the mean is 146, and standard deviation is 35. A score of 251 is how many z-scores above the mean? The following figure shows the normal distribution with the proportion of the area under the normal curve containedwithin one, two, and three standard

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the mean is 146, and standard deviation is 35. A score of 251 is how many z-scores above the mean?

The following figure shows the normal distribution with the proportion of the area under the normal curve contained
within one, two, and three standard deviations of the mean. The last proportion on each side, 0.13%, depicts the
remaining area under the curve. Specifically, 0.13% of the area under the standard normal distribution is located
above z-score values greater than the mean (P) plus three standard deviations (+30). Also, because the normal
distribution is symmetrical, 0.13% of the area under the standard normal distribution is located below z-score values
less than the mean (µ) minus three standard deviations (-30).
34.13%
34.13%
13.59%
13.59%
2.15%
2.15%
0.13%
0.13%
-30
-20
-10
+10
+20
+30
Use the figure to help you answer the following questions.
The National Assessment of Educational Progress (NAEP) is a nationwide assessment of students' proficiency in nine
subjects: mathematics, reading, writing, science, the arts, civics, economics, geography, and U.S. history. The main
NAEP assessments are conducted annually on samples of students from grades 4, 8, and 12.
the mean is 146. and standard deviation 35

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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