Final answer:
To find the mean, variance, and standard deviation of a probability distribution, you need to understand the formulas and steps involved. Sketching the distribution graph can help visualize the data. The probability of an event occurring can be calculated by summing up the probabilities of the desired outcomes.
Step-by-step explanation:
a. Sketch a graph of the probability distribution of X.
To sketch a graph of the probability distribution of X, we need to know the values of X and their corresponding probabilities. Once we have these values, we can plot them on a graph where the x-axis represents the values of X and the y-axis represents the probabilities.
b. Using the formulas, calculate the (i) mean and (ii) standard deviation of X.
To calculate the mean of X, we multiply each value of X by its probability, and then sum up the products. To calculate the standard deviation of X, we first find the deviation of each value of X from the mean, square each deviation, multiply each squared deviation by its probability, and then sum up the products. Finally, we take the square root of the sum to get the standard deviation.
c. Find the probability that more than five people in the sample are literate. Is it more likely that three people or four people are literate?
To find the probability that more than five people are literate, we need to sum up the probabilities of all values of X greater than five. To compare the probabilities that three people and four people are literate, we simply need to compare their individual probabilities.