We are looking at f(x)=λe-λx for 0≤x<∞ as the exponential probability function. In this exponential distribution mean μ=standard deviation σ=1/λ. f(x)=0 for x<0.
x is the value for which we need to calculate the probability, so x=μ+1.21/λ=(1/λ)(1+1.21)=2.21/λ. We need the cumulative probability for this value of x, which requires us to find the area beneath f(x) between x=0 and x=2.21/λ. The total area under f(x) is 1 (100%), the sum of all possible data. F(x)=∫f(x)dx=1-e-λx (after calculating the integration constant by using F(x→∞)=1), therefore the probability is 1-e-λ(2.21/λ)=1-e-2.21=0.8903 or about 89%. This is the percentage of the data that lies below 1.21 standard deviations of the mean.