Final answer:
The mean of a gamma distribution is given by the product of these parameters. Thus, the mean reaction time for formula B is α times β, which translates to 1 * 4 = 4 minutes.
Step-by-step explanation:
Reaction to Tear Gas: Let Y (in minutes) represent the length of time required to generate a human reaction to tear gas. Formula A follows a gamma distribution with parameters α = 2 and β = 2, while formula B also follows a gamma distribution with parameters α = 1 and β = 4.
Find the mean for formula BTo find the mean for formula B, we can use the formula for the mean of a gamma distribution: mean = α * β. For formula B, the values of α and β are 1 and 4, respectively. Therefore, the mean for formula B is 1 * 4 = 4.
The subject at hand is regarding the mean of a gamma distribution used to model the reaction time to tear gas. For formula B with parameters α = 1 and β = 4, the mean of a gamma distribution is given by the product of these parameters. Thus, the mean reaction time for formula B is α times β, which translates to 1 * 4 = 4 minutes.