Question
In: Statistics and Probability
Consider the following discrete probability distribution. x 15 22 34 40 P(X = x) 0.08 0.41...
Consider the following discrete probability
distribution.
| x | 15 | 22 | 34 | 40 |
| P(X = x) | 0.08 | 0.41 | 0.28 | 0.23 |
a. Is this a valid probability distribution?
-
Yes, because the probabilities add up to 1.
-
No, because the gaps between x values vary.
b. What is the probability that the random
variable X is less than 36? (Round your answer to
2 decimal places.)
c. What is the probability that the random
variable X is between 12 and 27? (Round your
answer to 2 decimal places.)
d. What is the probability that the random
variable X is greater than 20? (Round your answer
to 2 decimal places.)
Solutions
Expert Solution
Given
| x | 15 | 22 | 34 | 40 |
| P(X=x) | 0.08 | 0.41 | 0.28 | 0.23 |
a. Yes because the probabilities add up to 1.
i.e 
In discrete probability distribution random variable x tells about what are the possibile values x can take with some probability assigned to x and these probabilities add up to 1.
Therefore sum of all probabilities of x should be equal to 1.
b.To find the probability that the random variable X is less than 36.
Therefore,
The probability that the random variable X is less than 36 is 0.77
c.To find the probability that the random variable X is between 12 and 27.
Therefore,
The probability that the random variable X is between 12 and 27 is 0.49
d. To find the probability that the random variable X is greater than 20.
Therefore,
The probability that the random variable X is greater than 20 is 0.92.
orchestra answered 1 year agoRelated Solutions
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