In a recent year, the total scores for a certain standardized test were normally distributed, with a mean of 500 and a standard deviation of 10.3. Answer parts (a)-(d) below. (a) Find the probability that a randomly selected medical student who took the test had a total score that was less than 494. The probability that a randomly selected medical student who took the test had a total score that was less than 494 is. (Round to four decimal places as needed.) (b) Find the probability that a randomly selected medical student who took the test had a total score that was between 498 and 513. The probability that a randomly selected medical student who took the test had a total score that was between 498 and 513 is (Round to four decimal places as needed.) (c) Find the probability that a randomly selected medical student who took the test had a total score that was more than 529. The probability that a randomly selected medical student who took the test had a total score that was more than 529 is. (Round to four decimal places as needed.)

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In a recent year, the total scores for a certain standardized test were normally distributed, with a mean of 500 and a standard deviation of 10.3. Answer parts (a)–(d) below.

(a) Find the probability that a randomly selected medical student who took the test had a total score that was less than 494.

The probability that a randomly selected medical student who took the test had a total score that was less than 494 is ____.
(Round to four decimal places as needed.)

(b) Find the probability that a randomly selected medical student who took the test had a total score that was between 498 and 513.

The probability that a randomly selected medical student who took the test had a total score that was between 498 and 513 is ____.
(Round to four decimal places as needed.)

(c) Find the probability that a randomly selected medical student who took the test had a total score that was more than 529.

The probability that a randomly selected medical student who took the test had a total score that was more than 529 is ____.
(Round to four decimal places as needed.)

(d) Identify any unusual events. Explain your reasoning. Choose the correct answer below.

- A. None of the events are unusual because all the probabilities are greater than 0.05.
- B. The events in parts (a) and (b) are unusual because their probabilities are less than 0.05.
- C. The event in part (c) is unusual because its probability is less than 0.05.
- D. The event in part (a) is unusual because its probability is less than 0.05.
Transcribed Image Text:In a recent year, the total scores for a certain standardized test were normally distributed, with a mean of 500 and a standard deviation of 10.3. Answer parts (a)–(d) below. (a) Find the probability that a randomly selected medical student who took the test had a total score that was less than 494. The probability that a randomly selected medical student who took the test had a total score that was less than 494 is ____. (Round to four decimal places as needed.) (b) Find the probability that a randomly selected medical student who took the test had a total score that was between 498 and 513. The probability that a randomly selected medical student who took the test had a total score that was between 498 and 513 is ____. (Round to four decimal places as needed.) (c) Find the probability that a randomly selected medical student who took the test had a total score that was more than 529. The probability that a randomly selected medical student who took the test had a total score that was more than 529 is ____. (Round to four decimal places as needed.) (d) Identify any unusual events. Explain your reasoning. Choose the correct answer below. - A. None of the events are unusual because all the probabilities are greater than 0.05. - B. The events in parts (a) and (b) are unusual because their probabilities are less than 0.05. - C. The event in part (c) is unusual because its probability is less than 0.05. - D. The event in part (a) is unusual because its probability is less than 0.05.
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