Final answer:
a. Graph the distribution. b. Probability of testing 30 people. c. Probability of asking 10 people. d. Mean and standard deviation.
Step-by-step explanation:
a. Graph of the distribution:
To sketch the graph of the distribution of the discrete random variable X, we need to plot the values of X on the x-axis and the corresponding probabilities on the y-axis. Given that X takes on the values 0, 1, 2, 3, 4, 5, we can create a bar graph with these values. The height of each bar represents the probability of that value.
b. Probability of testing 30 people:
To find the probability of testing 30 people to find one with this disease, we need to sum the probabilities of testing x number of people until we find one with the disease. In this case, we need to sum the probabilities of testing 1 person, 2 people, 3 people, and so on, until 30 people. The probability can be calculated by substituting the value of x into the given probability distribution function, f(x), and summing the results.
c. Probability of asking 10 people:
Similar to the previous question, to find the probability of asking 10 people until we find one with the disease, we need to sum the probabilities of asking 1 person, 2 people, 3 people, and so on, until 10 people.
d. Mean and standard deviation:
i. Mean: The mean of the distribution can be calculated by multiplying each value of X by its corresponding probability, and then summing the results.
ii. Standard deviation: The standard deviation of the distribution can be calculated by first finding the variance, which is the sum of the squared differences between each value of X and the mean, multiplied by their corresponding probabilities. The standard deviation is then the square root of the variance.