Calculate the specified probability
-Suppose that $\mathrm { T }$ is a random variable. Given that $\mathrm { P } ( 3.5 \leq \mathrm { T } \leq 3.5 ) = 0.275$ , and that $\mathrm { P } ( \mathrm { K } < 3.5 ) = \mathrm { P } ( \mathrm { K } >$ 3.5) , find $\mathrm { P } ( \mathrm { K } < - 3.5 )$ .

Question

Calculate the specified probability
-Suppose that $\mathrm { T }$ is a random variable. Given that $\mathrm { P } ( 3.5 \leq \mathrm { T } \leq 3.5 ) = 0.275$, and that $\mathrm { P } ( \mathrm { K } < 3.5 ) = \mathrm { P } ( \mathrm { K } >$ 3.5), find $\mathrm { P } ( \mathrm { K } < - 3.5 )$.  
A)$0.3625$
B) $0.275$
C) $1.75$
D) $0.725$

Quizplus · Accepted Answer

Given that $P(3.5 \leq T \leq 3.5) = 0.275$, this implies that the probability of $T$ being exactly 3.5 is 0.275. Since $P(K < 3.5) = P(K > 3.5)$, the total probability for $K$ being less than or greater than 3.5 must sum to $1 - 0.275 = 0.725$, because probabilities sum to 1 and we subtract the probability of $K$ being exactly 3.5. Given the symmetry, $P(K < 3.5) = P(K > 3.5) = 0.725 / 2 = 0.3625$. Since $P(K < -3.5)$ is a subset of $P(K < 3.5)$ and the distribution is not specified, we assume the distribution is symmetric around 0, making $P(K < -3.5) = P(K > 3.5) = 0.3625$.

Calculate the Specified Probability -Suppose That T\mathrm { T }T Is a Random Variable

Calculate the Specified Probability
-Suppose That $\mathrm { T }$ Is a Random Variable