Final answer:
To create a probability distribution and histogram for the random variable z representing the sum of two dice, list the possible outcomes and their probabilities. Create a histogram by plotting the values of z and corresponding probabilities. The distribution resembles a bell curve.
Step-by-step explanation:
To create a probability distribution and construct a histogram for the random variable z, which represents the sum of the two numbers on a pair of dice, we first need to determine all the possible outcomes and their corresponding probabilities. Since each die has 6 sides, there are 36 possible outcomes when two dice are rolled. The values of the random variable z range from 2 to 12. The probability distribution is as follows:
P(z = 2) = 1/36, P(z = 3) = 2/36, P(z = 4) = 3/36, P(z = 5) = 4/36, P(z = 6) = 5/36, P(z = 7) = 6/36, P(z = 8) = 5/36, P(z = 9) = 4/36, P(z = 10) = 3/36, P(z = 11) = 2/36, P(z = 12) = 1/36
To create a histogram, we plot the values of z on the x-axis and the corresponding probabilities on the y-axis. Each bar represents the probability of a particular sum. The shape of the histogram will resemble a bell curve, with the highest bar at the center (for a sum of 7) and decreasing bars on either side.