# Poisson vs. normal approximation

• Nov 30th 2009, 04:43 AM
Intsecxtanx
Poisson vs. normal approximation
This is just a homework problem from the text that I can't seem to set up right.
Assume that the background noise X of a digital signal has a normal distribution with $\displaystyle \mu = 0$ volts and $\displaystyle \sigma = 0.5$ volt. If we observe n = 100 independent measurements of this noise, what is the probability that at least 7 of them exceed 0.98 in absolute value?

How would you use the Poisson distribution to approximate this probability?
Or the normal distribution to approximate this probability?

Thanks in advance. I was just wondering how one would go about setting this up.
• Nov 30th 2009, 06:28 AM
CaptainBlack
Quote:

Originally Posted by Intsecxtanx
This is just a homework problem from the text that I can't seem to set up right.
Assume that the background noise X of a digital signal has a normal distribution with $\displaystyle \mu = 0$ volts and $\displaystyle \sigma = 0.5$ volt. If we observe n = 100 independent measurements of this noise, what is the probability that at least 7 of them exceed 0.98 in absolute value?

How would you use the Poisson distribution to approximate this probability?
Or the normal distribution to approximate this probability?

Thanks in advance. I was just wondering how one would go about setting this up.

The mean number that exceed $\displaystyle 0.98$ in absolute value is $\displaystyle 5$ ($\displaystyle 0.98$v is $\displaystyle 1.96 \times \sigma$).

So the actual number that exceed $\displaystyle 0.98$v: $\displaystyle X \sim B(100,0.05).$

This has an approximate normal distribution $\displaystyle N(5,100\times 0.05 \times 0.95)$

Also this has an approximate Poisson distribution $\displaystyle \text{Pois}(5)$

CB