SAT : MEAN IS 500 STANDARD DEVIATION IS 100ACT: MEAN IS 20 STANDARD DEVIATION IS 6 What proportion of the population score above an 18 on the ACT?What proportion of students score below an 18 on the ACT?What is the ACT score associated with the top 10% of the population?What is the ACT score associated with the bottom 30% of the population?On the SAT, a student scores a 550 on the math subtest. On the ACT, the same student scores a 24 onthe math subtest. Did she perform better on the SAT or the ACT math sections? Be sure to explainvour reasoning and show any work you might do to answer this question.

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Description: SAT : MEAN IS 500 STANDARD DEVIATION IS 100ACT: MEAN IS 20 STANDARD DEVIATION IS 6 What proportion of the population score above an 18 on the ACT?What proportion of students score below an 18 on the ACT?What is the ACT score associated with the top 1

Given: Let X denote the SAT score thus, X~ N(500, 1002) Let Y denote the ACT score thus, Y~ N(20,…

Answered: What proportion of the population score…

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SAT : MEAN IS 500 STANDARD DEVIATION IS 100

ACT: MEAN IS 20 STANDARD DEVIATION IS 6

What proportion of the population score above an 18 on the ACT?
What proportion of students score below an 18 on the ACT?
What is the ACT score associated with the top 10% of the population?
What is the ACT score associated with the bottom 30% of the population?
On the SAT, a student scores a 550 on the math subtest. On the ACT, the same student scores a 24 on
the math subtest. Did she perform better on the SAT or the ACT math sections? Be sure to explain
vour reasoning and show any work you might do to answer this question.

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 + ...

Expert Solution

Step 1

Given:

Let X denote the SAT score thus, X~ N(500, 100²)

Let Y denote the ACT score thus, Y~ N(20, 6²)

Part 1:

The proportion of the population score above 18 on the ACT is computed as,

$P (Y > 18) = 1 - P (Y < 18) = 1 - P (\frac{X - μ}{σ} < \frac{18 - 20}{6}) = 1 - P (Z < - 0.3333) = 1 - 0.369454 = 0.630546$

Thus, the proportion of the population score above 18 on the ACT is 0.630546.

Part 2:

The proportion of the population score below 18 on the ACT is computed as,

$P (Y < 18) = 1 - P (Y > 18) = 1 - 0.630546 = 0.369454$

Thus, the proportion of the population score below 18 on the ACT is 0.369454.

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