## Normal Distribution- HELP!

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

### Normal Distribution- HELP!

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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Joined: Sun Jul 07, 2013 5:50 pm

### IB Maths SL Normal Distribution

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

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

By GDC (Casio) menu>STAT>DIST>NORM>Ncd with Lower:-9*10^99, Upper:475, $\sigma=20$, $\mu=450$ and you get
$P(X\leq475)=0.89435$

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

Here you have inverse normal

By GDC (Casio) menu>STAT>DIST>NORM>InvN with Tail:Right, Area:0.27, $\sigma=20$, $\mu=450$ 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

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, $\sigma=0.25$, $\mu=6.84$ and you get
q=6.5418337 and r=7.13816663

Hope these help!!
miranda

Posts: 268
Joined: Mon Jan 28, 2013 8:03 pm