# The probability distribution for the random variable x follows X. f (x) 20. 0.21 25. 0.13 30. 0.30 36 0.36 a) what is the probability that...

The probability distribution for the random variable x follows

X. f (x)

20. 0.21

25. 0.13

30. 0.30

36 0.36

a) what is the probability that x=30 ( to 2 decimals)?

b) what is the probability that x is less than or equal to 25 ( to 2 decimal)?

c) what is the probability that x is greater than 30 ( to 2 decimal places)?

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Using the given probability distribution of the discrete variable, x:

1) Probability that x =30 is given as **0.30** (can be directly read from the given data).

2) Probability that x is less than or equal to 25 = probability that x is less than 25 + probability that x is equal to 25 = 0.21 + 0.13 = **0.34**

3) Probability that x is greater than 30 = **0.36** (Same as probability of x =36, since this is the only value of x, greater than 30, for which the value of f(x) is given.).

We can also cross-check the overall result. The 3 statements account for the probabilities of the instances of x less than 30, x equal to 30 and x greater than 30; which should obviously be 1 (as it covers all the possible values of x). The same is the sum of probabilities of the three cases.

hope this helps.