(a) Find the probability that a randomly selected medical student who took the test had a total score that was less than 491. The probability that a randomly selected medical student who took the test had a total score that was less than 491 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 512. The probability that a randomly selected medical student who took the test had a total score that was between 498 and 512 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 528. The probability that a randomly selected medical student who took the test had a total score that was more than 528 is (Round to four decimal places as needed.)

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### Understanding Probability in Normally Distributed Test Scores

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 10.6. Answer parts (a)–(d) below.

#### Part (a)
**Task:** Find the probability that a randomly selected medical student who took the test had a total score that was less than 491.

**Probability Calculation:**

The probability that a randomly selected medical student who took the test had a total score that was less than 491 is \_\_\_\_.

_(Round to four decimal places as needed.)_

#### Part (b)
**Task:** Find the probability that a randomly selected medical student who took the test had a total score that was between 498 and 512.

**Probability Calculation:**

The probability that a randomly selected medical student who took the test had a total score that was between 498 and 512 is \_\_\_\_.

_(Round to four decimal places as needed.)_

#### Part (c)
**Task:** Find the probability that a randomly selected medical student who took the test had a total score that was more than 528.

**Probability Calculation:**

The probability that a randomly selected medical student who took the test had a total score that was more than 528 is \_\_\_\_.

_(Round to four decimal places as needed.)_

#### Part (d)
**Task:** Identify any unusual events. Explain your reasoning. Choose the correct answer below.

1. The events in parts (a) and (b) are unusual because their probabilities are less than 0.05.
2. The event in part (c) is unusual because its probability is less than 0.05.
3. None of the events are unusual because all the probabilities are greater than 0.05.
4. The event in part (a) is unusual because its probability is less than 0.05.

_Select the applicable answer(s) below:_
- A. \[\]
- B. \[\]
- C. \[\]
- D. \[\]

_Click to select your answer(s)._
Transcribed Image Text:### Understanding Probability in Normally Distributed Test Scores 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 10.6. Answer parts (a)–(d) below. #### Part (a) **Task:** Find the probability that a randomly selected medical student who took the test had a total score that was less than 491. **Probability Calculation:** The probability that a randomly selected medical student who took the test had a total score that was less than 491 is \_\_\_\_. _(Round to four decimal places as needed.)_ #### Part (b) **Task:** Find the probability that a randomly selected medical student who took the test had a total score that was between 498 and 512. **Probability Calculation:** The probability that a randomly selected medical student who took the test had a total score that was between 498 and 512 is \_\_\_\_. _(Round to four decimal places as needed.)_ #### Part (c) **Task:** Find the probability that a randomly selected medical student who took the test had a total score that was more than 528. **Probability Calculation:** The probability that a randomly selected medical student who took the test had a total score that was more than 528 is \_\_\_\_. _(Round to four decimal places as needed.)_ #### Part (d) **Task:** Identify any unusual events. Explain your reasoning. Choose the correct answer below. 1. The events in parts (a) and (b) are unusual because their probabilities are less than 0.05. 2. The event in part (c) is unusual because its probability is less than 0.05. 3. None of the events are unusual because all the probabilities are greater than 0.05. 4. The event in part (a) is unusual because its probability is less than 0.05. _Select the applicable answer(s) below:_ - A. \[\] - B. \[\] - C. \[\] - D. \[\] _Click to select your answer(s)._
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