Normal Distribution- HELP!

Algebra, Functions and equations, Circular functions and trigonometry, Vectors, Statistics and probability, Calculus. IB Maths SL Revision Notes

Normal Distribution- HELP!

Postby judIB » Sun Jul 07, 2013 6:07 pm

Questions:
1. A random variable X is distributed normally with mean 450 and standard deviation 20.
a). Find P(X<(or equal to)475)
b). Given that P(X>a)=0.27, find a.

2. The heights of certain plants are normally distributed. The plants are classified into three categories.
The shortest 12.92% are in category A.
The tallest 10.38% are in category C.
All the other plants are in category B with heights between r cm and t cm.
a). Diagram to represent this info.
b). Given that the mean height is 6.84 cm and the standard deviation 0.25cm, find the value of r and t
judIB
 
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IB Maths SL Normal Distribution

Postby miranda » Mon Jul 08, 2013 3:12 pm

IB Math SL Normal Distribution
Answers:
1. A random variable X is distributed normally with mean 450 and standard deviation 20.

a). Find P(X<(or equal to)475)

Answer:

By GDC (Casio) menu>STAT>DIST>NORM>Ncd with Lower:-9*10^99, Upper:475, , and you get




b). Given that P(X>a)=0.27, find a.
Answer:

Here you have inverse normal

By GDC (Casio) menu>STAT>DIST>NORM>InvN with Tail:Right, Area:0.27, , and you get
a=462.25626


2. The heights of certain plants are normally distributed. The plants are classified into three categories.
The shortest 12.92% are in category A.
The tallest 10.38% are in category C.
All the other plants are in category B with heights between r cm and t cm.
a). Diagram to represent this info.
b). Given that the mean height is 6.84 cm and the standard deviation 0.25cm, find the value of r and t

Answer:
P(q<B<r)=0.9

Again you have an inverse normal case with Area 100%-12.92%-10.38%=76.7%

By GDC (Casio) menu>STAT>DIST>NORM>InvN with Tail:Central, Area:0.767, , and you get
q=6.5418337 and r=7.13816663

Hope these help!! :) :)
miranda
 
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