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Given in the question that, a large machine is filled with thousands of small pieces of candy, $40\%$of which are orange. When money is deposited, the machine dispenses $60$randomly selected pieces of candy. The machine will be recalibrated if a group of $60$ candies contains fewer than 18 that are orange. We need to find the approximate probability that will happen if the machine is working correctly .

Thousands of small pieces of candy are stacked in a big machine, with orange candy accounting for $40\%$of the total. The issue here is population proportions. The issue is that $40\%$of the dollars are orange, indicating that the genuine population proportion is $0.4$. For proportions, the z-score formula is:

$z=\frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}}$

$=\frac{0.3-0.4}{\sqrt{\frac{0.4(1-0.4)}{60}}}$

The answer is option (a).