Dioxin, often described as the most toxic chemical known, is created as a by-product in the manufacture of herbicides such as Agent Orange. Scientists have found that .000005 gram (five-millionths of a gram) of dioxin—a dot barely visible to the human eye—is a lethal dose for experimental guinea pigs in more than half the animals tested, making dioxin 2,000 times more toxic than strychnine. Assume that the amount of dioxin required to kill a guinea pig has a relative frequency distribution with mean μ = .000005 gram and standard deviation σ = .000002 gram. Consider an experiment in which the amount of dioxin required to kill each of n = 50 guinea pigs is measured, and the sample mean is computed.

a. Calculate μ_y̅ and σ_y̅.

b. Find the probability that the mean amount of dioxin required to kill the 50 guinea pigs is larger than .0000053 gram.