# Normal Approximation to the Binomial Distribution

#### asantos

##### New Member
Hello everyone.

So, I was trying to solve some exercises on the normal distribution and the approximation of Normal to Binomial but I just can't seem to solve this exercise:
"It has been estimated that about 30% of frozen chickens contain enough salmonella bacteria to cause illness if improperly cooked. A supermarket has acquired 1000 frozen chickens.
a) What is the probability that at most 315 chickens are contamined?
b) What is the prob. that between 400 and 500 chickens are contaminated?"

Tried solution: first of all, I assumed the variable was Binomial, but since "np = 300 > 5" and "n(1-p)= 700 > 5", I tried to solve with the Normal approximation. X~N(300 (mean), 14.5 (standard deviation, rounded) )
a) P(X≤ 315)= P(Z≤ 315.5-300/14.5) = P(Z≤1.07) = 0.8577
b) P(400<X<500) = P(399.5-300/14.5 < Z < 500.5-300/14.5) = (6.86 < Z < 13.8) = ?

The table I use for the Normal dist. only goes up to 3.59, so I don't really know how to deal with the z values I got on b). Maybe I'm doing this all wrong?

I'd really appreciate it if someone could help! Thank you,

PS- sorry, english is not my first language, but I hope you can understand.