Consider the following discrete probability distribution.
x 15 22 34 40
P(X = x) 0.16 0.40 0.25 0.19
a. Is this a valid probability distribution?
multiple choice
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 39? (Round your answer to 2 decimal places.)
c. What is the probability that the random variable X is between 9 and 27? (Round your answer to 2 decimal places.)
d. What is the probability that the random variable X is greater than 19? (Round your answer to 2 decimal places.)
a. Yes, because the probabilities add up to 1.
b. To find the probability that X is less than 39, we need to sum up the probabilities for all x values less than 39.
P(X < 39) = P(X = 15) + P(X = 22) + P(X = 34)
= 0.16 + 0.40 + 0.25
= 0.81
Therefore, the probability that X is less than 39 is 0.81.
c. To find the probability that X is between 9 and 27, we need to sum up the probabilities for all x values between 9 and 27.
P(9 < X < 27) = P(X = 15) + P(X = 22)
= 0.16 + 0.40
= 0.56
Therefore, the probability that X is between 9 and 27 is 0.56.
d. To find the probability that X is greater than 19, we need to sum up the probabilities for all x values greater than 19.
P(X > 19) = P(X = 22) + P(X = 34) + P(X = 40)
= 0.40 + 0.25 + 0.19
= 0.84
Therefore, the probability that X is greater than 19 is 0.84.
a. Yes, because the probabilities add up to 1.
b. To find the probability that X is less than 39, we sum up the probabilities for x values less than 39:
P(X < 39) = P(X = 15) + P(X = 22) + P(X = 34) = 0.16 + 0.40 + 0.25 = 0.81
Therefore, the probability that X is less than 39 is 0.81.
c. To find the probability that X is between 9 and 27, we sum up the probabilities for x values between 9 and 27:
P(9 < X < 27) = P(X = 15) + P(X = 22) = 0.16 + 0.40 = 0.56
Therefore, the probability that X is between 9 and 27 is 0.56.
d. To find the probability that X is greater than 19, we sum up the probabilities for x values greater than 19:
P(X > 19) = P(X = 22) + P(X = 34) + P(X = 40) = 0.40 + 0.25 + 0.19 = 0.84
Therefore, the probability that X is greater than 19 is 0.84.
a. To determine if this is a valid probability distribution, we need to check if the probabilities add up to 1. Let's calculate the sum of the probabilities:
0.16 + 0.40 + 0.25 + 0.19 = 1
The sum of the probabilities is indeed 1, so this is a valid probability distribution. Therefore, the correct answer is: Yes, because the probabilities add up to 1.
b. To find the probability that the random variable X is less than 39, we need to sum the probabilities of all the values less than 39. In this case, we sum the probabilities of x = 15, 22, and 34:
P(X < 39) = P(X = 15) + P(X = 22) + P(X = 34) = 0.16 + 0.40 + 0.25 = 0.81
The probability that X is less than 39 is 0.81.
c. To find the probability that the random variable X is between 9 and 27, we need to sum the probabilities of all the values between 9 and 27. In this case, we sum the probabilities of x = 15 and 22:
P(9 < X < 27) = P(X = 15) + P(X = 22) = 0.16 + 0.40 = 0.56
The probability that X is between 9 and 27 is 0.56.
d. To find the probability that the random variable X is greater than 19, we need to sum the probabilities of all the values greater than 19. In this case, we sum the probabilities of x = 22, 34, and 40:
P(X > 19) = P(X = 22) + P(X = 34) + P(X = 40) = 0.40 + 0.25 + 0.19 = 0.84
The probability that X is greater than 19 is 0.84.