Question: Suppose that $T$ is a random variable. Given that $P(-3.3 \leq T \leq 3.3) =.775$, and that $P(T<-3.3)=P(T > 3.3)$, we are to find $P(T < -3.3)$.
How do I begin to solve this?
The answer is .1125
$\endgroup$ 32 Answers
$\begingroup$If $P(-3.3 \le T \le 3.3)$ and $P(T > 3.3) = P(T < -3.3)$ for a random variable $T,$ then find $P(T < - 3.3).$
Can you figure out why the probability not in the center has to be split in half and finish the problem?
$\endgroup$ 1 $\begingroup$$\mathbb P (-3.3<=T<=3.3) = 0.775$
$\mathbb P(T<-3.3)$ indicates probability from -infinity to $-3.3$
$\mathbb P(T>3.3)$ indicates probability from 3.3 to +infinity
Let the $\mathbb P(T<-3.3) = x = \mathbb P(T>3.3)$
$\mathbb P(T<-3.3) + \mathbb P(-3.3<=T<=3.3) + \mathbb P(T>3.3) = 1$
$2x + 0.775 = 1$
$x = 0.1125$
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