In a recent year, Delaware had the highest per capita annual income with $51,803. If o=$4850, find the mean X that falls at the 95th percentile for a sample of 35 residents.

Z = (score-mean)/SEm

SEm = SD/√n

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability (.95) and its Z score. Insert Z score into top equation to calculate score.

To find the mean (X) that falls at the 95th percentile for a sample of 35 residents, we need to follow these steps:

Step 1: Calculate the z-score corresponding to the 95th percentile.
A z-score represents the number of standard deviations a particular data point is from the mean. We can use z-scores to find percentiles in a standard normal distribution. The 95th percentile corresponds to a z-score of approximately 1.645.

Step 2: Use the formula for the z-score:
z = (X - μ) / (σ / √n)
where:
X = mean
μ = population mean
σ = population standard deviation
n = sample size

Step 3: Rearrange the formula to solve for X:
X = μ + (z * (σ / √n))

Step 4: Substitute the given values into the formula:
Given:
o = $4850 (population standard deviation)
n = 35 (sample size)
μ = $51,803 (income per capita for Delaware)

X = $51,803 + (1.645 * ($4850 / √35))
X ≈ $51,803 + (1.645 * $819.08)
X ≈ $51,803 + $1346.36
X ≈ $53,149.36

Therefore, the mean X that falls at the 95th percentile for a sample of 35 residents is approximately $53,149.36.