Answer
(a) For a valid probability probability distribution, we must have total probability equal to 1
So, sum of all f(x) values must equal to 1
0.25+0.17+0.27+0.31 = 1
So, it is a valid probability distribution because sum is equal to 1.
(b) Using the above data table, it is given in the table that the probability value correspondin to x value of 32 is 0.27
So, required probability is 0.27
(c) Probability of x less than or equal to 24, i.e. it means sum of probability of 20 and 24
So, using the above data table, we can write
Required probability = P(20) + P(24) = 0.25+0.17 = 0.42
So, required probability is 0.42 (rounded to 2 decimal places)
(d) Probability of x greater than or equal to 32 means the sum of probability of 32 and 35
So, using the above data table, we can write
Required probability = P(32) + P(35) = 0.27+0.31 = 0.58
So, required probability is 0.58 (rounded to 2 decimal places)
The probability distribution for the random variable x follows. 20 24 32 35 f(x) 0.25 0.17...
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