The number of bytes downloaded per second on an information channel has mean 10⁵ and standard deviation 10⁴. Among the factors influencing the rate is congestion, which produces alternating periods of faster and slower transmission. Let X represent the number of bytes downloaded in a randomly chosen five-second period.

a. Is it reasonable to assume that μ_X = 5 × 10⁵? Explain.

b. Is it reasonable to assume that σ_X =√5 × 10⁴? Explain.