IB Maths SL Normal Distribution

IB Mathematics SL Normal Distribution
Answers:

1. random variable X normally distributed with mean 25.
The shaded region between 25 and 27 represents 30% of the distribution.
a). Find P(X>27)
Answer:


b). Find the standard deviation of X
Answer:
Let the random variable X , so that



We know that

Since we don’t know the standard deviation of X, we cannot use the inverse normal. Therefore we have to transform the random variable to that of

, using the transformation

we have the following





Using GDC Casio fx-9860G SD
MAIN MENU > STAT>DIST(F5)>NORM(F1)>InvN>

Setting Tail: right
Area: 0.2
:1
:0

We find that the standardized value is 0.8416

Therefore



2. A random variable X is distributed normally with a mean of 20 and variance 9.
a). Find P(X<(or equal to)24.5)
Answer:

By GDC (Casio) menu>STAT>DIST>NORM>Ncd with Lower:-9*10^99, Upper:24.5, , and you get


b). Let P(X<(or equal to)k)=0.85
ii). Find the value of k.
Answer:

Here you have inverse normal

By GDC (Casio) menu>STAT>DIST>NORM>InvN with Tail:Left, Area:0.85, , and you get

Question and Answer can be found here

http://www.ibmaths4u.com/viewtopic.php?f=11&t=372