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To solve this problem, we need to use the properties of the normal distribution along with the standard normal (Z) transformation. The normal distribution is continuous, symmetric, and fully described by its mean (μ) and standard deviation (σ). Here, the mean μ = 534 cm, standard deviation σ = 13.5 cm, and total number of observations N = 1000. Step 1: Observations exceeding 561 cm First, we calculate the Z-score for 561 cm using the formula: $$ Z = \frac{X - \mu}{\sigma} $$ Where X is the value of interest. Substituting the values: $$ Z = \frac{561 - 534}{13.5} = \frac{27}{13.5} = 2 $$ A Z-score of 2 ________ ________ _________ __________ _________ ____ ____ _____ _______ ___ _______ ____.
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