Final answer:
To find the area to the right of x = 38 under the normal distribution with mean 36 and standard deviation 6, calculate the z-score using Z = (X - μ) / σ, then subtract the area to the left of this z-score from 1.
Step-by-step explanation:
To find the area to the right of x = 38 under a normal distribution curve with μ = 36 and σ = 6, you first need to calculate the z-score. The formula for the z-score is:
Z = (X - μ) / σ
Substituting our values in, we get:
Z = (38 - 36) / 6 = 2 / 6 = 0.3333
Next, you use the z-score to find the area to the left of x using a z-table, calculator, or software that can compute areas under the normal curve. If you have the z-table handy, you would look up the z-score of 0.3333 and find the corresponding area to the left of that z-score. To find the area to the right (which is what we are interested in), you subtract the area to the left from 1:
Area to the right of x = 38 = 1 - Area to the left of z = 0.3333