Question 1094175: 2. A random variable X follows a continuous distribution, which is symmetric to 0. If P(X ≤-3)= 0.2, then which of the following statements are true? (There are more than one true statements) SHOW WORK
(a) P(X≤-4)≤0.2
(b) P(-3≤X≤3)=0.6
(c) P(X≤-2)≤0.2
(d) P(X≥3)=0.8
Answer by greenestamps(13200)   (Show Source):
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Since the distribution is continuous and symmetric about 0, P(x<=-3) = 0.2 means P(x>=3) = 0.2 also. That makes answer (d) false. It also means P(-3<=x<=3) = (1-0.2-0.2) = 0.6. So answer (b) is a true statement.
Answer (a) says P(x<=-4) is less than 0.2. If P(x<=-3) is equal to 0.2 and the distribution is continuous, the P(x<=-4) must be less than 0.2. So (a) is a true statement.
By similar reasoning, statement (c) is not true; if P(x<=-3) = 0.2 and the distribution is continuous, then p(x<=-2) must be greater than 0.2.
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