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The conditions for the Central Limit Theorem conditions for sample proportions are: \n\n1. The sampling method is simple random sampling. It is stated in the problem that we are taking a random sample of 100 high school seniors, so this condition is met. 2. The samples are independent. Since the sample size of 100 is less than 10% of all high school seniors (assuming there are more than 1,000 high school seniors), we can assume independence. 3. There are at least 10 successes and failures in the population. Since 72% of the high school seniors have driver’s licenses, it means that at least 72 out of 100 succeeded in getting a drivers license, and at least 28 out of 100 do not have a driver’s license. Hence, this condition is satisfied.

The mean of the sample proportion is equal to the population proportion, which is 0.72. The standard deviation, denoted as σ, of a sampling distribution is calculated by: \[σ = \sqrt{ \frac{p(1-p)}{n}}\] where p is the population proportion and n is the sample size. Inserting the values, we get standard deviation as: \[σ = \sqrt{\frac{0.72(1 - 0.72)}{100}} = 0.045\]

The Z-score measures how many standard deviations an observation is away from the mean. Here, we need to calculate the Z-score for the sample proportion of 0.75 (75%), which is greater than the population mean. The Z-score is calculated by: \[Z = \frac{p - P}{σ}\] where p is the sample proportion, P is population proportion and σ is standard deviation of the sample. Inserting the values, we get Z-score as: \[Z = \frac{0.75 - 0.72}{0.045} = 0.67\]

We needed to find the probability that the poprortion is more than 0.75 (ie. \(P(p>0.75)\)), which can be found by finding the area to the right of the Z-score (0.67) using Z-table or any statistics software/tool. The area to the right of z-score 0.67 is \(0.2514\), so, the probability that more than 75% of the students have a driver’s license is around 0.2514 or 25.14%.