a. To complete the probability distribution, we need to find the missing probability value.
Since the sum of all probabilities must equal 1, we can subtract the sum of the given probabilities from 1 to find the missing probability value:
1 - 0.36 - 0.08 - 0.18 = 0.38
Therefore, the complete probability distribution is:
x −15 −5 10 25
P(X = x) 0.36 0.08 0.38 0.18
b. To find the probability that the random variable X is negative, we sum the probabilities for x = -15 and x = -5:
P(X < 0) = P(X = -15) + P(X = -5) = 0.36 + 0.08 = 0.44
Therefore, the probability that the random variable X is negative is 0.44.
c. To find the probability that the random variable X is greater than -10, we sum the probabilities for x = 10 and x = 25:
P(X > -10) = P(X = 10) + P(X = 25) = 0.38 + 0.18 = 0.56
Therefore, the probability that the random variable X is greater than -10 is 0.56.
d. To find the probability that the random variable X is less than 25, we sum the probabilities for x = -15, x = -5, and x = 10:
P(X < 25) = P(X = -15) + P(X = -5) + P(X = 10) = 0.36 + 0.08 + 0.38 = 0.82
Therefore, the probability that the random variable X is less than 25 is 0.82.
Consider the following discrete probability distribution.
x −15 −5 10 25
P(X = x) 0.36 0.08 0.18
a. Complete the probability distribution. (Round your answer to 2 decimal places.)
b. What is the probability that the random variable X is negative? (Round your answer to 2 decimal places.)
c. What is the probability that the random variable X is greater than −10? (Round your answer to 2 decimal places.)
d. What is the probability that the random variable X is less than 25? (Round your answer to 2 decimal places.)
1 answer