An elementary class rarely remains the same size from the beginning of the school year until the end. Families move in and out of the district, some students are reassigned, and scheduling conflicts necessitate changes. Suppose the change in the number of students in a class is a random variable with probability distribution given by
a. Verify that this is a valid probability distribution.
b. Find the mean, variance, and standard deviation of the change in class size.
c. Suppose two classes are selected at random. Find the probability that both classes remain the same size for the entire year.
Many organizations publish wedding guidelines with specific suggestions regarding the reception, wedding cake, flowers, and even themes and styles. However, the number of bridesmaids and groomsmen is usually a very personal decision made by the bride and groom. For semiformal weddings, one to six bridesmaids are typical, with a possible flower girl and/or ring bearer.16 Suppose the probability distribution for the number of bridesmaids at a semiformal wedding is given in the table below.
a. Find the mean, variance, and standard deviation for the number of bridesmaids at a semiformal wedding.
b. Suppose a randomly selected semiformal wedding has at least four bridesmaids. What is the probability that it has exactly six bridesmaids?
c. Suppose four semiformal weddings are randomly selected. What is the probability that all four have at least three bridesmaids?