Final answer:
To answer this question, we need to sketch the graph of the probability distribution, calculate probabilities for specific scenarios, and find the mean and standard deviation of the distribution.
Step-by-step explanation:
a. To sketch the graph, we plot the values of X on the x-axis and the corresponding probabilities on the y-axis. The points on the graph represent the values and probabilities given in the probability distribution table.
b. The probability of finding one person with the disease after testing 30 people can be found by summing the probabilities of testing 1 to 30 people without finding someone with the disease.
c. The probability of finding one person with the disease after asking 10 people can be found by summing the probabilities of asking 1 to 10 people without finding someone with the disease.
d.(i) The mean of X, denoted as E(X), can be found by multiplying each value of X by its corresponding probability, and then summing the products.
d.(ii) The standard deviation of X measures the spread of the distribution around the mean and can be calculated using the formula: sqrt(sum((x - mean)^2 * p(x)))