1.) Two dice are rolled and the sum is calculated. Let X represent the sum of the two dice. Construct a probability distribution expressing probabilities in fractional form.
2.) Find the mean and standard deviation to 2 decimal places for problem #1.
3.) On the basis of past experience an insurance salesperson knows that the number of long-term health care insurance policies sold per week by the company is a random variable x with the following probability distribution.
X p(x)
0 0.245
1 0.143
2 0.125
3 0.096
4 0.078
5 0.064
6 0.039
7 0.029
8 0.181
Suppose that a week is randomly selected. Find
a.) p(x=3) b.) p(x > 4) c.) p(x < 8) d.) p(1 < x < 6)
4.) A question on a proficiency test is multiple choices with five possible answers, one of which is correct. Assuming that all responses are random guesses, find the probability that among 18 test subjects,
a.) exactly 5 answer the question correctly.
b.) at most 6 answer the question correctly.
c.) at least 8 answer the question correctly.
5.) Referring back to question 4, find the mean to the nearest hundredth and the standard deviation to four decimal places.