**Understanding Probability in Standardized 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 10.2. This exercise consists of four parts (a-d) to explore the probabilities related to this distribution.**(a) Probability of Scoring Less Than 487** - **Scenario:** Determine the probability that a randomly selected medical student who took the test had a total score that was less than 487. - **Answer:** The probability formulation for this scenario is: > The probability that a randomly selected medical student who took the test had a total score that was less than 487 is ____. (Round to four decimal places as needed.)**(b) Probability of Scoring Between 496 and 510** - **Scenario:** Find the probability that a randomly selected medical student who took the test had a total score that was between 496 and 510. - **Answer:** The probability formulation for this scenario is: > The probability that a randomly selected medical student who took the test had a total score that was between 496 and 510 is ____. (Round to four decimal places as needed.)**(c) Probability of Scoring More Than 523** - **Scenario:** Find the probability that a randomly selected medical student who took the test had a total score that was more than 523. - **Answer:** The probability formulation for this scenario is: > The probability that a randomly selected medical student who took the test had a total score that was more than 523 is ____. (Round to four decimal places as needed.)**(d) Identifying Unusual Events** - **Task:** Identify any unusual events and explain your reasoning. - **Options:** 1. The events in part (a) and (b) are unusual because their probabilities are less than 0.05. 2. The events in part (a) and (c) are unusual because their probabilities are less than 0.05. 3. The events in part (b) and (c) are unusual because their probabilities are less than 0.05. 4. No probability is less than 0.05, so no event is unusual.For more detailed analysis, one might consider the usage of Z-scores and standard normal distribution tables or computational tools to derive these 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 10.2. Answer parts (a)–(d) below.(a) The probability that a randomly selected medical student who took the test had a total score that was between 496 and 510 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 523.(d) The probability that a randomly selected medical student who took the test had a total score that was more than 523 is [ ].(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 (b) are unusual because their probabilities are less than 0.05.- B. The event in part (a) is unusual because its probability is less than 0.05.- C. The event in part (c) is unusual because its probability is less than 0.05.- D. None of the events are unusual because all the probabilities are greater than 0.05.In this exercise, students are expected to calculate the probabilities using statistical methods for normally distributed data.

The random variable X follows normal distribution. The population mean is 500. The population…

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 10.2. 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 487. The probability that a randomly selected medical student who took the test had a total score that was less than 487 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 496 and 510. The probability that a randomly selected medical student who took the test had a total score that was between 496 and 510 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 523. The probability that a randomly selected medical student who took the test had a total score that was more than 523 is (Round to four decimal places as needed.) (d) Identify any unusual events. Explain your reasoning. Choose the correct answer below.

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 10.2. 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 487. The probability that a randomly selected medical student who took the test had a total score that was less than 487 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 496 and 510. The probability that a randomly selected medical student who took the test had a total score that was between 496 and 510 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 523. The probability that a randomly selected medical student who took the test had a total score that was more than 523 is (Round to four decimal places as needed.) (d) Identify any unusual events. Explain your reasoning. Choose the correct answer below.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

**Understanding Probability in Standardized 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 10.2. This exercise consists of four parts (a-d) to explore the probabilities related to this distribution.

**(a) Probability of Scoring Less Than 487**
- **Scenario:** Determine the probability that a randomly selected medical student who took the test had a total score that was less than 487.
- **Answer:** The probability formulation for this scenario is:
> The probability that a randomly selected medical student who took the test had a total score that was less than 487 is ____. (Round to four decimal places as needed.)

**(b) Probability of Scoring Between 496 and 510**
- **Scenario:** Find the probability that a randomly selected medical student who took the test had a total score that was between 496 and 510.
- **Answer:** The probability formulation for this scenario is:
> The probability that a randomly selected medical student who took the test had a total score that was between 496 and 510 is ____. (Round to four decimal places as needed.)

**(c) Probability of Scoring More Than 523**
- **Scenario:** Find the probability that a randomly selected medical student who took the test had a total score that was more than 523.
- **Answer:** The probability formulation for this scenario is:
> The probability that a randomly selected medical student who took the test had a total score that was more than 523 is ____. (Round to four decimal places as needed.)

**(d) Identifying Unusual Events**
- **Task:** Identify any unusual events and explain your reasoning.
- **Options:**
1. The events in part (a) and (b) are unusual because their probabilities are less than 0.05.
2. The events in part (a) and (c) are unusual because their probabilities are less than 0.05.
3. The events in part (b) and (c) are unusual because their probabilities are less than 0.05.
4. No probability is less than 0.05, so no event is unusual.

For more detailed analysis, one might consider the usage of Z-scores and standard normal distribution tables or computational tools to derive these

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 10.2. Answer parts (a)–(d) below.

(a) The probability that a randomly selected medical student who took the test had a total score that was between 496 and 510 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 523.

(d) The probability that a randomly selected medical student who took the test had a total score that was more than 523 is [ ].
(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 (b) are unusual because their probabilities are less than 0.05.
- B. The event in part (a) is unusual because its probability is less than 0.05.
- C. The event in part (c) is unusual because its probability is less than 0.05.
- D. None of the events are unusual because all the probabilities are greater than 0.05.

In this exercise, students are expected to calculate the probabilities using statistical methods for normally distributed data.

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