Answer to Question #303097 in Statistics and Probability for Trix

Question #303097

Suppose the IQ of the learners in a certain University follows a normal distribution with

mean 110 and standard deviation 100?

a What proportion of the learners population have IQ's more than 90 but less than 100?

b. A random male learner is selected from this University. What is the chance that his IQ is more than 136?

c Stacy de leon, a Physics major, is prolific writer and a Math genius of this

university. If it is known that Stacy's IQ belongs to the upper 1% of the learner

population, what is her minimum IQ?


1
Expert's answer
2022-03-01T12:09:03-0500

Suppose the IQ of the learners in a certain University follows a normal distribution with mean 110 and standard deviation 10

a


P(90<X<100)=P(Z<10011010)P(90<X<100)=P(Z<\dfrac{100-110}{10})

P(Z9011010)=P(Z<1)P(Z2)-P(Z\le\dfrac{90-110}{10})=P(Z<-1)-P(Z\le-2)

0.1586550.022750=0.1359\approx0.158655-0.022750=0.1359

b.


P(X>136)=1P(Z13611010)P(X>136)=1-P(Z\le\dfrac{136-110}{10})

=1P(Z13611010)=1-P(Z\le\dfrac{136-110}{10})

=1P(Z2.6)=0.004661=1-P(Z\le2.6)=0.004661

c.


P(X>x)=0.01P(X>x)=0.01

1P(Zx11010)=0.011-P(Z\le\dfrac{x-110}{10})=0.01

P(Zx11010)=0.99P(Z\le\dfrac{x-110}{10})=0.99

x11010=2.326348\dfrac{x-110}{10}=2.326348

x=133.26x=133.26

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