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 40th percentile of the time it takes college students to find a parking spot in the library. Round to 1 decimal:

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 40th percentile of the time it takes college students to find a parking spot in the library.

Step 3 ：The 40th percentile of a distribution is the value below which 40% of the data falls. Since the distribution is normal, we can use the standard normal distribution to find this value.

Step 4 ：The Z-score corresponding to the 40th percentile can be found using a Z-table or a function like scipy's ppf (percent point function).

Step 5 ：Once we have the Z-score, we can convert it back to the original scale using the formula: \(X = \mu + Z\sigma\) where \(X\) is the value in the original scale, \(\mu\) is the mean, \(Z\) is the Z-score, and \(\sigma\) is the standard deviation. In this case, \(\mu = 5.0\) minutes and \(\sigma = 2\) minutes.

Step 6 ：Substituting the values into the formula, we get \(X = 5.0 + (-0.2533471031357997) * 2.0\)

Step 7 ：Solving the equation, we get \(X = 4.493305793728401\)

Step 8 ：Rounding to 1 decimal place, we get \(X = 4.5\)

Step 9 ：Final Answer: The 40th percentile of the time it takes college students to find a parking spot in the library is approximately \(\boxed{4.5}\) minutes.