Answered: Suppose that the IQs of university A's…

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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Question

Suppose that the IQs of university A's students can be described by a normal model with mean 140 and standard deviation 6 points. Also suppose that IQs of students from university B can be described by a normal model with mean 130 and standard deviation 11.

a) Select a student at random from university A. Find the probability that the student's IQ is at least

135 points.

The probability is ? (Round to three decimal places as needed.)

b) Select a student at random from each school. Find the probability that the university A student's IQ is at least

5 points higher than the university B student's IQ.

The probability is ? (Round to three decimal places as needed.)

c) Select 3 university B students at random. Find the probability that this group's average IQ is at least

140 points.

The probability is ? (Round to three decimal places as needed.)

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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