Word Count : 542

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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 indicates that 561 cm is 2 standard deviations above the mean. Using standard normal distribution tables, the area to the left of Z = 2 is approximately _________ ____ ______ ______ _____.
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