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.)
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.
a. To complete the probability distribution, we need to find the missing probability. The sum of probabilities in a probability distribution must be equal to 1.
Sum of given probabilities: 0.36 + 0.08 + 0.18 = 0.62
The missing probability is: 1 - 0.62 = 0.38
Complete probability distribution:
x -15 -5 10 25
P(X=x) 0.36 0.08 0.38 0.18
b. The probability that the random variable X is negative can be found by summing 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. The probability that the random variable X is greater than -10 can be found by summing 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. The probability that the random variable X is less than 25 can be found by summing 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.
a. To complete the probability distribution, we need the sum of all probabilities P(X=x) to be equal to 1. We can see that there is a missing probability value in the table. To find this missing probability, we subtract the sum of the given probabilities from 1:
1 - (0.36 + 0.08 + 0.18) = 1 - 0.62 = 0.38
So, the missing probability for the value 10 is 0.38. Completing the probability distribution, we have:
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 need to sum the probabilities for all the negative values of X:
P(X < 0) = P(X = -15) + P(X = -5)
So, the probability that the random variable X is negative is:
P(X < 0) = 0.36 + 0.08 = 0.44
c. To find the probability that the random variable X is greater than -10, we need to sum the probabilities for all the values of X greater than -10:
P(X > -10) = P(X = 10) + P(X = 25)
So, the probability that the random variable X is greater than -10 is:
P(X > -10) = 0.38 + 0.18 = 0.56
d. To find the probability that the random variable X is less than 25, we need to sum the probabilities for all the values of X less than 25:
P(X < 25) = P(X = -15) + P(X = -5) + P(X = 10)
So, the probability that the random variable X is less than 25 is:
P(X < 25) = 0.36 + 0.08 + 0.38 = 0.82