Final answer:
The value x=91.6 is approximately 2.85 standard deviations to the right of the mean (μ=87.9) on a normal distribution curve when the standard deviation is σ=1.3. This puts it well into the tail of the curve, indicating it's an unusually high value for this distribution.
Step-by-step explanation:
To determine where the given x=91.6 value would be on the curve, we first consider the given mean (μ=87.9) and standard deviation (σ=1.3). A normal distribution curve is symmetric around the mean, and standard deviation measures the spread of the data from the mean.
The value x=91.6 is higher than the mean, so it will lie to the right of the center of the curve. To find out how many standard deviations away x is from the mean, we calculate the z-score using the formula:
z = (x - μ) / σ
Substituting the given values:
z = (91.6 - 87.9) / 1.3
z = 3.7 / 1.3
z ≈ 2.85
This means that x=91.6 is approximately 2.85 standard deviations to the right of the mean on the curve. In a normal distribution, this placement is well into the tail, indicating that x=91.6 is an unusually high value relative to this distribution.