Answered: A teachers’ analysis of statistics…

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 teachers’ analysis of statistics exams found the exam scores had a normal distribution with mean µ = 70 and a standard deviation σ = 5. The passing cutoff for the exam is one standard deviation below the mean, or µ − σ.
(a) In a class with 60 students, how many students will pass? Draw a normal curve and shade in the relevant area, and be sure to indicate how you calculated the relevant area.
(b) Suppose the teacher will give an A to anyone whose score is at least 2 standard deviations above the mean (so scores above µ + 2σ). How many students (of the same 60) will get an A in this case?

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 :

$μ = 70$

$σ = 5$

passing cutoff for the exam is one standard deviation below the mean, or µ − σ.

n = 60

$P (X < μ - σ) = P (X < 65)$

$P (X < μ - σ) = P (\frac{X - μ}{σ} < \frac{65 - 70}{5})$

$P (X < μ - σ) = P (z < - 1)$

$P (X < μ - σ) = 0.1587 u \sin g z t a b l e$

$N u m b e r o f s t u d e n t w i l l b e p a s s = n \times p$

$N u m b e r o f s t u d e n t w i l l b e p a s s = 60 \times 0.1587$

$N u m b e r o f s t u d e n t w i l l b e p a s s = 9.52 \approx 10$

In a class with 60 students, 10 students will pass.

Step 2

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