Answer to Question #303097 in Statistics and Probability for Trix

Question

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?

Answer 1

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

a

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

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

$$\approx0.158655-0.022750=0.1359$$

b.

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

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

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

c.

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

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

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

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

$$x=133.26$$