A spinner with four equal sectors labeled "purple,” "blue,” "orange,” and "green” is spun 45 times. What is the probability that the spinner will land on "purple” in fewer than 20% of the spins?Find the z-table here.

The probability of landing on purple in one spin is 1/4 = 0.25. For 45 spins, the standard deviation of the sample proportion is √(0.25 × 0.75 ÷ 45) ≈ 0.0645. The z-score for a proportion of 0.20 is (0.20 − 0.25) ÷ 0.0645 ≈ −0.77, which has a lower-tail probability of about 0.221. So the answer is 0.221, choice B.

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