## Statistics Normal Distribution

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

### Statistics Normal Distribution

Continuous Probability Distribution, Normal Distribution - IB Maths HL

How can we find the mean $\mu$
of the weight of a population of students which is found to be normally distributed with standard deviation 2.5 Kg and the 20% of the students weigh at least 54 Kg.

Thanks
lora

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

### Re: Statistics Normal Distribution

Statistics Normal Distribution - IB Mathematics HL

Let the random variable $S$ denotes the weight of the students, so that

$S \sim N( \mu, (2.5)^2)$

We know that $P(S \geq 54)=0.2$

Since we don’t know the mean, we cannot use the inverse normal. Therefore we have to transform the random variable $S$ to that of

$Z\sim N(0,1)$ , using the transformation $Z= \frac{S- \mu}{\sigma}$

we have the following

$P(S \geq 54)=0.2 \Rightarrow P(\frac{S- \mu}{\sigma} \geq \frac{54- \mu}{2.5})=0.2$

$\Rightarrow P(Z \geq \frac{54- \mu}{2.5})=0.2$

Using GDC Casio fx-9860G SD

Setting Tail: right
Area: 0.2
$\sigma$:1
$\mu$:0

We find that the standardized value is 0.84162123

Therefore
$\frac{54- \mu}{2.5}=0.84162123\Rightarrow 54- \mu =2.104053$

$\mu=53- 2.104053 =50.9 (3 s.f.)$

Hope these help!
lily

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

### Re: Statistics Normal Distribution

Thanks Lily!!
lora

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