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 probability that a randomly selected college student takes more than 4.5 minutes to find a parking spot in the library. Round your solution to 4 decimals:
Answer
Final Answer: The probability that a randomly selected college student takes more than 4.5 minutes to find a parking spot in the library is approximately \(\boxed{0.5987}\).
Step 1 ：The problem is asking for the probability that a randomly selected college student takes more than 4.5 minutes to find a parking spot. This is a problem of normal distribution. We know that the mean (\(\mu\)) is 5.0 minutes and the standard deviation (\(\sigma\)) is 2 minutes.
Step 2 ：We need to find the z-score for 4.5 minutes. The z-score is calculated by subtracting the mean from the value and dividing by the standard deviation. In this case, \(z = \frac{4.5 - 5.0}{2.0} = -0.25\).
Step 3 ：Next, we need to find the area to the right of this z-score on the standard normal distribution curve, which represents the probability we are looking for. The probability corresponding to z = -0.25 is approximately 0.5987.
Step 4 ：Final Answer: The probability that a randomly selected college student takes more than 4.5 minutes to find a parking spot in the library is approximately \(\boxed{0.5987}\).
