A standardized exam's scores are normally distributed. In a recent year, the mean test score was1485and the standard deviation was313.The test scores of four students selected at random are1900,1210,2190,and1380.Find the z-scores that correspond to each value and determine whether any of the values are unusual.The z-score for1900isnothing.(Round to two decimal places as needed.)The z-score for1210isnothing.(Round to two decimal places as needed.)The z-score for2190isnothing.(Round to two decimal places as needed.)The z-score for1380isnothing.(Round to two decimal places as needed.)Which values, if any, are unusual? Select the correct choice below and, if necessary, fill in the answer box within your choice. A.The unusual value(s) is/arenothing.(Use a comma to separate answers as needed.) B.None of the values are unusual.

Answered: A standardized exam's scores are…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A standardized exam's scores are normally distributed. In a recent year, the mean test score was

1485

and the standard deviation was

313.

The test scores of four students selected at random are

1900,

1210,

2190,

and

1380.

Find the z-scores that correspond to each value and determine whether any of the values are unusual.

The z-score for

1900

nothing.

(Round to two decimal places as needed.)

The z-score for

1210

nothing.

(Round to two decimal places as needed.)

The z-score for

2190

nothing.

(Round to two decimal places as needed.)

The z-score for

1380

nothing.

(Round to two decimal places as needed.)

Which values, if any, are unusual? Select the correct choice below and, if necessary, fill in the answer box within your choice.

The unusual value(s) is/are

nothing.

(Use a comma to separate answers as needed.)

None of the values are unusual.

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

It is given that the mean score, $μ$ of a standardized test is equal to 1485 and the standard deviation, $σ$ is equal to 313

Z-score of an individual data point denotes how many standard deviations it is away from the mean of the population. This helps in understanding if a data value is an unusual value or not

The z-score can be calculated using the formula, $z = \frac{x - μ}{σ}$ , where z is the z-score, x is the individual data point, $μ$ is the mean and $σ$ is the standard deviation

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