Question

The probability distribution for the random variable x follows. 20 24 32 35 f(x) 0.25 0.17 0.27 0.31 a. Is this a valid probability distribution? Select b. What is the probability that x 32 (to 2 decimals)? c. What is the probability that x is less than or equal to 24 (to 2 decimals)? d. What is the probability that x is greater than 32 (to 2 decimals)?

Answer 1

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)