The probability distribution for the number of insurance policies is as follows:

x0123

p(x).44.20.18.18

Find the mean, variance, standard deviation, expected value, and draw the histogram.

2) Let x be the number of evens we can roll with a random die. Is this a probability distribution? Why or why not?

3) Suppose that the probabilities are .2, .4, .3, and .1 that the number of wills filed on any day at Polk County Courthouse will be 0, 1, 2, or 3.

a) Draw a probability distribution chart and find the mean, variance, and standard deviation.

b) What is the probability of at least 2 wills being filed?

c) What is the probability that at most 1 will is filed?

4) The instructor of a large class gives 15% each of Aâ€™s and Dâ€™s, 30% each of Bâ€™s and Câ€™s, and 10% Fâ€™s. Choose a student at random from this class. The studentâ€™s grade on a four-point scale is a random variable X.

a) Draw the probability distribution chart

b) Find the mean grade

c) Calculate the probability that a randomly selected student will get a grade of B or better.

5) The Tri-State Pick 3 Lottery game offers a choice of several bets. You choose a 3-digit number. The lottery pays $83.33 if the number you chose has the same digits as the winning number, in any order. Find the expected payoff for a $1 bet (assume that you choose a number having 3 different digits).