The lifetimes of 10,000 watch batteries are normally distributed the mean lifetime is 500 days the standard deviation is 60 days sketch a normal curve that represents this distribution label the mean and 3 standard deviations

Given:

μ = 500 days, the population mean

σ = 60 days, the population standard deviation

Therefore

μ + σ = 560

μ - σ = 440

μ + 2σ = 620

μ - 2σ = 380

μ + 3σ = 680

μ - 3σ = 320

The figure shown below illustrates the normal distribution

About 68% of the total area lies in x = (μ-σ, μ+σ)

About 95% of the total area lies in x = (μ-2σ, μ+2σ)

About 99.7% of the total area lies in x = (μ-3σ, μ+3σ).