# Thread: Poisson vs. normal approximation

1. ## 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 $\mu = 0$ volts and $\sigma = 0.5$ 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.

2. 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 $\mu = 0$ volts and $\sigma = 0.5$ 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 $0.98$ in absolute value is $5$ ( $0.98$v is $1.96 \times \sigma$).

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

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

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

CB