There is a 32.81% chance (0.3182) that there will be between 32647 and 43559 ants on a randomly chosen acre.
The Z-score calculates how far a measure deviates from the mean by standard deviation. We look at the p-value linked with this Z-score after determining the Z-score by consulting the z-score table. This p-value represents the likelihood that the measure's value is less than X, or the percentile of X. We may calculate the likelihood that the value of the measure exceeds X by subtracting 1 from the pvalue.
The zscore of a measure X in a set with mean and standard deviation may be calculated as follows:
Z= X-μ/σ
μ = 42000 σ= 12275
The pvalue of Z when X = 32647 is deducted from the pvalue of Z when X = 43559 to get this value. So
X = 43559
z= 0.13 has a pvalue of 0.5517
X = 32647
z= -0.76 has a pvalue of 0.2236
0.5517 - 0.2236 = 0.3281
0.3182 = 32.81% probability that a randomly selected acre has between 32647 and 43559 ants.
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