Juries should have the same racial distribution as the surrounding communities. about % of residents in a certain region are a specific race. suppose a local court randomly selects 250250 adult citizens of the region to participate in the jury pool. use the central limit theorem (and the empirical rule) to find the approximate probability that the proportion of available jurors of the above specific race is more than twotwo standard errors from the population value of 0.220.22. the conditions for using the central limit theorem are satisfied because the sample is random; the population is more than 10 times 250250; n times p is , and n times (1 minus p) is 195195, and both are more than 10. fill in the blanks below. because the sampling distribution for the sample proportion is approximately normal, it is known that the probability of falling within twotwo standard errors is about ▼ .68. 0.997. 0.95. therefore, the probability of falling more than twotwo standard errors away from the mean is about ▼ 0.05. 0.003. 32.