IQ is normally distributed with a mean of 100 and a standard deviation of 15. Suppose one individual is randomly chosen. Let X = IQ of an individual.Part (a)Give the distribution of X.X ~ N = Part (b)Find the probability that the person has an IQ greater than 135.Write the probability statement.P = . What is the probability? (Round your answer to four decimal places.)Sketch the graph. Part (c)Mensa is an organization whose members have the top 2% of all IQs. Find the minimum IQ needed to qualify for the Mensa organization.Write the probability statement.P(X > x) =What is the minimum IQ? (Round your answer to the nearest whole number.)x =Sketch the graph.

Mean(µ) = 100Standard deviations (σ) = 15 Let X = IQ of an individual.

Answered: IQ is normally distributed with a mean…

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

IQ is normally distributed with a mean of 100 and a standard deviation of 15. Suppose one individual is randomly chosen. Let X = IQ of an individual.

Part (a)

Give the distribution of X.
X ~ N
=
Part (b)

Find the probability that the person has an IQ greater than 135.

Write the probability statement.

P =

.

What is the probability? (Round your answer to four decimal places.)

Sketch the graph.
Part (c)

Mensa is an organization whose members have the top 2% of all IQs. Find the minimum IQ needed to qualify for the Mensa organization.

Write the probability statement.

P(X > x) =

What is the minimum IQ? (Round your answer to the nearest whole number.)
x =

Sketch the graph.

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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