A variable is normally distributed with mean 20 and standard deviation 9. Use your graphing calculator to find each of the following areas. Write your answers in decimal form. Round to the nearest thousandth as needed.
a) Find the area to the left of 20.
b) Find the area to the left of 16 .
c) Find the area to the right of 18 .
d) Find the area to the right of 24 .
e) Find the area between 16 and 29 .

Step 1 ：The problem is asking for the area under the curve of a normal distribution. This is equivalent to finding the cumulative distribution function (CDF) at a certain point. The CDF at a point x for a normal distribution with mean μ and standard deviation σ is given by the formula: \(CDF(x) = 0.5 * (1 + erf((x - μ) / (σ * sqrt(2))))\) where erf is the error function.

Step 2 ：For part a), the area to the left of 20 is simply the CDF at 20. So, the area to the left of 20 is \(0.5\).

Step 3 ：For part b), the area to the left of 16 is the CDF at 16. So, the area to the left of 16 is \(0.328\).

Step 4 ：For part c), the area to the right of 18 is 1 - CDF(18) because the total area under the curve is 1. So, the area to the right of 18 is \(0.588\).

Step 5 ：For part d), the area to the right of 24 is 1 - CDF(24). So, the area to the right of 24 is \(0.328\).

Step 6 ：For part e), the area between 16 and 29 is CDF(29) - CDF(16). So, the area between 16 and 29 is \(0.513\).

Step 7 ：Final Answer: a) The area to the left of 20 is \(\boxed{0.5}\). b) The area to the left of 16 is \(\boxed{0.328}\). c) The area to the right of 18 is \(\boxed{0.588}\). d) The area to the right of 24 is \(\boxed{0.328}\). e) The area between 16 and 29 is \(\boxed{0.513}\).