Final answer:
Unfortunately, without specific frequencies for hours parked or amounts charged, we cannot calculate the expected parking time or the statistics for the fees charged. The normal distribution indicates it would be surprising to find a parking space in less than one minute. The question suggests the distribution of parking space times is likely non-uniform.
Step-by-step explanation:
Calculating Expected Parking Time and Fees Statistics
To calculate the expected time a customer parks, we need to multiply each number of hours by its corresponding frequency and then divide by the total number of drivers. However, since we do not have the specific frequencies for hours parked, we cannot perform this calculation.
For the variance and standard deviation of fees, these statistics describe the spread of the fees around the mean fee. We would calculate the variance by finding the mean fee, then subtracting this mean from each fee, squaring the result, and taking the average of these squared differences. The standard deviation is the square root of the variance. Without the specific amounts charged, we cannot calculate these values either.
If the amount charged is linearly related to the hours parked (e.g., a constant rate per hour), we could infer that the amount charged would increase with more hours parked.
Understanding Parking Space Time Distribution
Given that the time it takes to find a parking space follows a normal distribution with a mean of five minutes and a standard deviation of two minutes:
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- It would be surprising to find a parking space in less than one minute as it is more than two standard deviations away from the mean.
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- Option I is correct: the data cannot follow the uniform distribution if the mean is significantly greater than the standard deviation. This is because a uniform distribution would have a mean closer to its central point.
The length of time to find a parking space being heavily skewed to one side suggests the possibility of a non-uniform distribution.