We are given a normal distribution with mean μ = 7.1 and standard deviation σ = 1.3. We want to find the area to the right of x = 3.4. First, we calculate the z-score corresponding to x = 3.4 using the formula:
z = (x - μ) / σ
z = (3.4 - 7.1) / 1.3
z = -3.7 / 1.3
z = -2.846153846...
We are asked not to round, so we keep the full z-score.
Using a z-table or calculator, we find the area to the left of z = -2.846153846. We will denote this area as P(Z < -2.846153846).
A z-table gives us:
P(Z < -2.84) = 0.00226
P(Z < -2.85) = 0.00219
We can use linear interpolation to estimate P(Z < -2.846153846) ≈ 0.00222
Alternatively, we can use a calculator or statistical software to find the more precise value of P(Z < -2.846153846) ≈ 0.00221752739
Since the shaded area is to the _right_ of x = 3.4 (and correspondingly, to the right of z = -2.846153846), we need to find the area to the right of the z-score. Because the total area under the normal distribution curve is 1, we can calculate the shaded area as follows:
Shaded area = 1 - P(Z < -2.846153846) = 1 - 0.00221752739 = 0.99778247261
Answered
