Question 2 The length of time it takes college students to find a parking spot in the library parking lot follows a normal distribution with a mean of 5.0 minutes and a standard deviation of 2 minute. Find the percentile rank of a college student that takes 4.0 minutes to find a parking spot in the library lot. Round your solution to the nearest percentile:

Step 1 ：The length of time it takes college students to find a parking spot in the library parking lot follows a normal distribution with a mean of 5.0 minutes and a standard deviation of 2 minutes.

Step 2 ：We are asked to find the percentile rank of a college student that takes 4.0 minutes to find a parking spot in the library lot.

Step 3 ：The percentile rank of a score is the percentage of scores in its frequency distribution that are equal to or lower than it. In the context of a normal distribution, this is also known as the cumulative distribution function (CDF).

Step 4 ：To find the percentile rank of a college student that takes 4.0 minutes to find a parking spot, we need to calculate the CDF at 4.0 minutes.

Step 5 ：The CDF at a given value x for a normal distribution with mean μ and standard deviation σ is calculated as follows: \(CDF(x) = 0.5 * (1 + erf((x - μ) / (σ * sqrt(2))))\), where erf is the error function.

Step 6 ：Substituting the given values into the formula, we get \(CDF(4.0) = 0.5 * (1 + erf((4.0 - 5.0) / (2.0 * sqrt(2))))\).

Step 7 ：Calculating the above expression, we find that the percentile rank is 31.

Step 8 ：Final Answer: The percentile rank of a college student that takes 4.0 minutes to find a parking spot in the library lot is \(\boxed{31}\).