# How can I calculate these normal distribution exercises

I got to calculate the value for the variable $c$ when they give me this intervals but I don't know how to interpret the inequations.

a) $P(-c \le z \le c) = .668$.

b) $P(c \le |z|) = .016$.

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What are $n$ and $p$? – ncmathsadist Oct 7 '12 at 23:56
Are you using tables of the normal distribution, or software? – André Nicolas Oct 8 '12 at 0:02
I got to use the tables at last, I just would like to clear what is the right value I got to look for on the table to know c – diegoaguilar Oct 8 '12 at 0:04
Binomial distribution isn't defined on negative values. – Alex Oct 8 '12 at 0:26
Ok. any other parameters are known, like mean..? Can we state then, that it is about a normal distribution instead of binomial? – Berci Oct 8 '12 at 0:54

## 1 Answer

So. We have a probability variable $z$: some random thing happens, and then $z$ gets a value, assumed as a real number.

If this 'random thing' occurs according to a given distribution, then the corresponding distribution function is defined as: $$F(t):=P(z<t)$$ If the distribution is continuous, then all single points have zero probability, so $F(t)=P(z\le t)$. And, (assumed that $z$ has value with $1$ probability:) we also have $P(z>t) = 1-P(z\le t)$.

In your case, if you have given a continuous distriution by $F$, then $$\text{a) }\ P(-c\le z\le c) = F(c)-F(-c)$$ $$\text{b) }\ P(c\le|z|) = P((z\ge c)\lor(z\le -c))=1-F(c) + F(-c)$$

Now, if it happens to be the standard normal distribution (that is, in a sense a limit of binomial distributions), then $F=\Phi$ and you can also use its symmetry: $\Phi(-c) = 1-\Phi(c)$.

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