Step-by-step explanation:
The standard deviation of the earnings per common share for the past 5 years can be calculated using the formula:
σ = sqrt [ Σ ( Xi - μ )^2 / N ]
where σ is the standard deviation, Xi is the earnings per common share for each year, μ is the mean earnings per common share, and N is the number of observations.
To calculate the mean earnings per common share, we add up the earnings for the past 5 years and divide by 5:
μ = (2.68 + 1.03 + 2.26 + 4.30 + 3.58) / 5
μ = 2.57
Next, we calculate the variance by plugging in the values for each year:
σ^2 = [ (2.68 - 2.57)^2 + (1.03 - 2.57)^2 + (2.26 - 2.57)^2 + (4.30 - 2.57)^2 + (3.58 - 2.57)^2 ] / 5
σ^2 = 2.1216
Finally, we take the square root of the variance to get the standard deviation:
σ = sqrt (2.1216)
σ = 1.457
Therefore, the standard deviation of the earnings per common share for the past 5 years is 1.457.
If we assume that the distribution of earnings per common share is symmetrical and bell-shaped, about 95% of the observations will be between the mean plus and minus two standard deviations. So, the range of values that contain 95% of the observations is:
μ ± 2σ
2.57 ± 2(1.457)
2.57 ± 2.914
The lower limit is 2.57 - 2.914 = -0.344, which is not a meaningful value for earnings per common share. Therefore, we can assume that the range of values that contain 95% of the observations is:
2.57 ± 2.914
between 2.57 - 2.914 = -0.344 and 2.57 + 2.914 = 5.484.