1. A chemical supply company ships a certain solvent in 10-gallon drums. Let X represent the number of drums ordered by a randomly chosen customer. Assume X has the following probability mass function (pmf). The mean and variance of X is 2.3 and 1.81 respectively.
X 1 2 3 4 5
p(X=x) 0.4 0.2 0.2 0.1 0.1
(a) Find P(X<2) and describe what it means in the context of the problem.
(b) Let Y be the number of gallons ordered, so Y = 10X . Find the probability mass function (pmf) of Y.
(c) Find the mean number of gallons ordered μY using the pmf from part (b) and a second time using the expectectation of linear combination formula shown in class.
(d) Find the standard deviation of the number of gallons ordered Y using the pmf from part (b) and a second time using the standard deviation of linear combinationformulas shown in class.
(e) What possible values of Y are within two standard deviations of the mean value (that is, in the interval from (μ - 2SD, μ + 2SD ? What is the probability that the observed value of Y is within two standard deviations of the mean value?