**Field**: Mathematics

1) A student is randomly selected from a group of elementary school students. There are 10 six-year old students, 12 seven-year old students, 6 eight-year old students, 4 nine-year old students, and 8 ten-year old students.
a) Construct a probability distribution for the age of a randomly selected student.
b) Determine the expected value of the variable (same as the mean).
2) a) Determine the missing probability from the distribution shown below.
b) Determine the expected value of the variable (same as the mean).
x 0 1 2 3 4 5
P(x) 0.1 0.35 0.2 0.18 ? 0.05
3) Is the random variable discrete or continuous?
a) the number of births at a given hospital in one day.
b) the amount of water in a tub sitting outside during a storm.
4) Identify the shape of the binomial probability distribution for n = 10, and given success probability:
a) p = 0.25 b) p = 0.9
For Problem numbers 5 through 7: Eight students are randomly selected from the students at a large high school. One-third of the students in the school are freshman. The remaining two-thirds are not.
5) a) Explain why this experiment can be considered to be a binomial probability experiment.
b) Identify a “success” and specify the values of n, p, and q.
6) a) Construct a probability distribution for the number of randomly selected freshmen. b) Determine the expected value of the variable (same as the mean).
7) a) Determine the probability that at least one of the eight students are freshmen.
b) Determine the probability that at least two of the students are freshman.