If we know that the length of time it takes an MBA student to find a parking spot near the DePaul Center follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute, find the point in the distribution that 75.8% of the MBA students exceed when trying to find a parking spot.

Z = (score-mean)/SD

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to the Z score. Substitute the Z value in the above equation and solve for the score.

To find the point in the distribution that 75.8% of the MBA students exceed when trying to find a parking spot, we can use the concept of the standard normal distribution.

1. First, we convert the given normal distribution to a standard normal distribution by using the formula:

Z = (X - μ) / σ

Where:
- Z is the standard score
- X is the given value
- μ is the mean of the distribution
- σ is the standard deviation of the distribution

In this case, the given value is 3.5 minutes, the mean is 3.5 minutes, and the standard deviation is 1 minute.

Z = (X - μ) / σ
Z = (3.5 - 3.5) / 1
Z = 0

2. We then look up the corresponding area/probability in the standard normal distribution table. In this case, we're interested in finding the point that 75.8% of the students exceed, which means we want to find the point where 24.2% (100% - 75.8%) is below it.

Using the standard normal distribution table, we can find the Z-score that corresponds to the cumulative probability of 24.2%. In most tables, probabilities are given for values on the left side of the mean, so we need to subtract our probability from 1 to get the area to the right of our value.

Looking up the value closest to 24.2%, we find that the Z-score is approximately -0.71.

3. Finally, we use the Z-score we found to convert it back to the original scale of the distribution using the formula:

X = Z * σ + μ

X = -0.71 * 1 + 3.5
X = 2.79

Therefore, approximately 75.8% of the MBA students exceed a time of 2.79 minutes when trying to find a parking spot near the DePaul Center.