Final answer:
a. Sketch a graph of the probability distribution of X. b. Calculate the mean and standard deviation of X. c. Find the probability of more than five people being literate.
Step-by-step explanation:
a. Sketch a graph of the probability distribution of X:
In order to sketch the graph of the probability distribution of X for the standard normal distribution, we need to plot the values of X on the x-axis and the corresponding probabilities on the y-axis. The graph will be a bell-shaped curve centered around the mean of 0 with a standard deviation of 1.
b. Using the formulas, calculate the (i) mean and (ii) standard deviation of X:
The mean of X for the standard normal distribution is 0 and the standard deviation is 1.
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?
The probability of more than five people in the sample being literate can be found by subtracting the cumulative probability of five or less from 1. It is more likely that four people are literate than three people, as the probability of four people being literate is higher than the probability of three people being literate.