## Normal Distribution Statistics

Discussions for the Core part of the syllabus. Algebra, Functions and equations, Circular functions and trigonometry, Vectors, Statistics and probability, Calculus. IB Maths HL Revision Notes

### Normal Distribution Statistics

Statistics Normal Distribution - IB Maths HL

How can we find the percentage of the population will benefit from a new tax law
expected to benefit families with income between $15,000 and$30,000 given that the family income follows a normal distribution with mean $40,000 and standard deviation$15,000 ?

Thanks
lora

Posts: 0
Joined: Wed Apr 10, 2013 7:36 pm

### Re: Normal Distribution Statistics

Statistics, Normal Distribution - IB Mathematics HL

Let the random variable F denote the family income, so that

$F\sim N( 40,000, 15,000 ^2)$

the probability is

$P(15,000 \leq F \leq 30,000)$

Using GDC Casio fx-9860G SD

Setting Lower: 15,000
Upper: 30,000
$\sigma$: 15,000
$\mu$: 40,000

We find that the probability is 0.2047

Therefore, 20.5% of the families will benefit from this new tax law.

Hope these help!!
lily

Posts: 0
Joined: Mon Jan 28, 2013 8:04 pm

### Re: Normal Distribution Statistics

Thanks Lily!!
lora

Posts: 0
Joined: Wed Apr 10, 2013 7:36 pm