Since Nicole is taking a sample of 56 students, she may obtain a sample proportion that is different from the true population proportion of 73%. The range of sample proportions that Nicole is likely to obtain can be calculated using confidence intervals.
Assuming a normal distribution for the sample proportion, the 95% confidence interval can be calculated as:
p ± 1.96 * sqrt(p*(1-p)/n)
where:
p is the population proportion (given as 0.73)
n is the sample size (given as 56)
1.96 is the z-score for a 95% confidence level (which is a standard value used in statistics)
Substituting the given values, we get:
0.73 ± 1.96 * sqrt(0.73*(1-0.73)/56)
= 0.73 ± 0.112
Therefore, Nicole is likely to obtain sample proportions in the range of 0.618 to 0.842 (or equivalently, 61.8% to 84.2%). This means that if Nicole were to take many random samples of 56 students from the school, 95% of the sample proportions she obtains would fall within this range.