Answer:
To determine the number of boys expected to be taller than 6 inches, we need to calculate the proportion of boys taller than 6 inches and then multiply it by the total number of boys in the school.
First, we need to convert the height of 6 inches to a z-score using the formula:
z = (x - μ) / σ
Where:
x = value we want to convert to a z-score (6 inches)
μ = mean of the distribution (67 inches)
σ = standard deviation of the distribution (3.5 inches)
z = (6 - 67) / 3.5 = -61 / 3.5 ≈ -17.43
Next, we can use a standard normal distribution table or a calculator to find the proportion of boys taller than 6 inches, which corresponds to the area under the curve to the right of the z-score -17.43.
Looking up the z-score of -17.43 in a standard normal distribution table, we find that the area to the right of this z-score is essentially 0.
Therefore, we can expect that approximately 0 boys out of the 793 would be taller than 6 inches.
Step-by-step explanation:
