To achieve an 86% probability that the actual hours needed to finish his project will be less than or equal to the estimated hours, Stefan needs to identify the z-score associated with the 86th percentile of the standard normal distribution curve.
Identify the z-score: Using a standard normal distribution table or a statistical calculator, find the z-score that corresponds to an 86% probability. This z-score is approximately 1.0803.
Apply the z-score formula: The z-score formula is: z= (X-μ)/σ,where X is the estimated value, μ is the mean, and σ is the standard deviation.
Rearrange the formula to solve for X (estimated hours): Since Stefan wants an 86% probability, the z-score (1.0803) corresponds to the estimated hours on the bell curve. The mean (μ) in a standard normal distribution is 0, and the standard deviation (σ) is 1.
X=z×σ+μ
X=1.0803×1+0
X=1.0803
Therefore, Stefan should select the value of approximately 1.0803 on the bell curve as his estimated hours to achieve an 86% probability that the actual hours needed will be less than or equal to this estimation.