Questions: The probability that the study participant selected at random is less than 66 inches tall is .1711 . (Round to four decimal places as needed.) (b) Find the probability that a study participant has a height that is between 66 and 72 inches. The probability that the study participant selected at random is between 66 and 72 inches tall is .5378 . (Round to four decimal places as needed.) (c) Find the probability that a study participant has a height that is more than 72 inches. The probability that the study participant selected at random is more than 72 inches tall is .2912 . (Round to four decimal places as needed.) (d) Identify any unusual events. Explain your reasoning. Choose the correct answer below. A. The events in parts (a) and (c) are unusual because its probabilities are less than 0.05 . B. The events in parts (a), (b), and (c) are unusual because all of their probabilities are less than 0.05 . C. The event in part (a) is unusual because its probability is less than 0.05 . D. There are no unusual events because all the probabilities are areater than 0.05 .

The probability that the study participant selected at random is less than 66 inches tall is .1711 . (Round to four decimal places as needed.) (b) Find the probability that a study participant has a height that is between 66 and 72 inches. The probability that the study participant selected at random is between 66 and 72 inches tall is .5378 . (Round to four decimal places as needed.) (c) Find the probability that a study participant has a height that is more than 72 inches. The probability that the study participant selected at random is more than 72 inches tall is .2912 . (Round to four decimal places as needed.) (d) Identify any unusual events. Explain your reasoning. Choose the correct answer below. A. The events in parts (a) and (c) are unusual because its probabilities are less than 0.05 . B. The events in parts (a), (b), and (c) are unusual because all of their probabilities are less than 0.05 . C. The event in part (a) is unusual because its probability is less than 0.05 . D. There are no unusual events because all the probabilities are areater than 0.05 .
Transcript text: The probability that the study participant selected at random is less than 66 inches tall is .1711 . (Round to four decimal places as needed.) (b) Find the probability that a study participant has a height that is between 66 and 72 inches. The probability that the study participant selected at random is between 66 and 72 inches tall is .5378 . (Round to four decimal places as needed.) (c) Find the probability that a study participant has a height that is more than 72 inches. The probability that the study participant selected at random is more than 72 inches tall is .2912 . (Round to four decimal places as needed.) (d) Identify any unusual events. Explain your reasoning. Choose the correct answer below. A. The events in parts (a) and (c) are unusual because its probabilities are less than 0.05 . B. The events in parts (a), (b), and (c) are unusual because all of their probabilities are less than 0.05 . C. The event in part (a) is unusual because its probability is less than 0.05 . D. There are no unusual events because all the probabilities are areater than 0.05 .
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Solution

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Solution Steps

Step 1: Given Probabilities

The probabilities for the heights of study participants are as follows:

  • The probability that a participant is less than 66 inches tall is \( P(X < 66) = 0.1711 \).
  • The probability that a participant is between 66 and 72 inches tall is \( P(66 < X < 72) = 0.5378 \).
  • The probability that a participant is more than 72 inches tall is \( P(X > 72) = 0.2912 \).
Step 2: Assessing Unusual Events

To determine if any of these events are unusual, we check if their probabilities are less than \( 0.05 \):

  • For \( P(X < 66) = 0.1711 \): This is not unusual since \( 0.1711 > 0.05 \).
  • For \( P(66 < X < 72) = 0.5378 \): This is not unusual since \( 0.5378 > 0.05 \).
  • For \( P(X > 72) = 0.2912 \): This is not unusual since \( 0.2912 > 0.05 \).
Step 3: Conclusion on Unusual Events

Since all calculated probabilities are greater than \( 0.05 \), we conclude that there are no unusual events among the heights of the study participants.

Final Answer

The answer is \( \boxed{D} \) (There are no unusual events because all the probabilities are greater than 0.05).

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