The actual weight of the cans follows a uniform distribution between 9.3 ounces and 10.3 ounces. To compute the standard deviation for a uniform distribution, we can use the formula:
Standard Deviation (σ) = (b – a) / √12
Where:
- a is the minimum value (9.3 ounces).
- b is the maximum value (10.3 ounces).
Plugging in the values:
σ = (10.3 – 9.3) / √12
σ = 1.0 / √12
σ = 1.0 / 3.4641
σ ≈ 0.2887 ounces
Therefore, the standard deviation of the weight of the soup can is approximately 0.29 ounces. This value gives us an idea of how much the weights vary around the advertised weight of 10 ounces.