What is P(4 ≤ X ≤ 6)? Explain. If P(X ≤ a) = 0.2, what is a? Explain.

Question

~Questions 1 & 2~

Here is a Probability Distribution.

Look at the image below to answer the question, please.

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https://us-static.z-dn.net/files/d29/a97245f96d0a098056cba18c86ecab63.png

Answer 1

This is a simple but continuous probability distribution, the uniform distribution on the interval [2,7].

The random variable can only assume values between 2 and 7

The probability of any specific number is 0, e.g. P(X=.5)=0

and the probability that X falls in any interval is equal to (1/5)*length of the interval.

The answer to the first part is 2/5 and the answer to the second question is 3.