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) $P(c \le |z|) = .016$.
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) $P(c \le |z|) = .016$.
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
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: $\Phi(-c) = 1-\Phi(c)$.