↑ 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. (a) Find the probability that a randomly selected medical student who took the test had a total score that was less than 493. The probability that a randomly selected medical student who took the test had a total score that was less than 493 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 511. The probability that a randomly selected medical student who took the test had a total score that was between 496 and 511 is. (Round to four decimal places as needed.)
↑ 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. (a) Find the probability that a randomly selected medical student who took the test had a total score that was less than 493. The probability that a randomly selected medical student who took the test had a total score that was less than 493 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 511. The probability that a randomly selected medical student who took the test had a total score that was between 496 and 511 is. (Round to four decimal places as needed.)
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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Question
![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.
(a) Find the probability that a randomly selected medical student who took the test had a total score that was less than 493.
The probability that a randomly selected medical student who took the test had a total score that was less than 493 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 511.
The probability that a randomly selected medical student who took the test had a total score that was between 496 and 511 is [ ].
(Round to four decimal places as needed.)
---
**Explanation:**
For this set of questions, you need to apply your understanding of normal distribution. Given the mean (500) and the standard deviation (10.6), you can use the Z-score formula to find probabilities.
1. **Z-score formula:**
\[
Z = \frac{(X - \mu)}{\sigma}
\]
Where \( X \) is the score, \( \mu \) is the mean, and \( \sigma \) is the standard deviation.
2. **Part (a):** Determine the Z-score for a score of 493 and then use the standard normal distribution table to find the probability.
3. **Part (b):** Calculate the Z-scores for scores 496 and 511, find their corresponding probabilities from the standard normal distribution table, and compute the difference to find the probability of a score falling between these two values.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F275f078e-e6df-4549-aae8-3195dc20960c%2F3942f78c-c88d-4951-a4d7-f65655e78edd%2Fe4zy3p_processed.jpeg&w=3840&q=75)
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 10.6. 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 493.
The probability that a randomly selected medical student who took the test had a total score that was less than 493 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 511.
The probability that a randomly selected medical student who took the test had a total score that was between 496 and 511 is [ ].
(Round to four decimal places as needed.)
---
**Explanation:**
For this set of questions, you need to apply your understanding of normal distribution. Given the mean (500) and the standard deviation (10.6), you can use the Z-score formula to find probabilities.
1. **Z-score formula:**
\[
Z = \frac{(X - \mu)}{\sigma}
\]
Where \( X \) is the score, \( \mu \) is the mean, and \( \sigma \) is the standard deviation.
2. **Part (a):** Determine the Z-score for a score of 493 and then use the standard normal distribution table to find the probability.
3. **Part (b):** Calculate the Z-scores for scores 496 and 511, find their corresponding probabilities from the standard normal distribution table, and compute the difference to find the probability of a score falling between these two values.
![The image shows a multiple-choice question on evaluating the probability of events in the context of medical student test scores.
---
**Question:**
(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:
- **O A.** None of the events are unusual because all probabilities are greater than 0.05.
- **O B.** The event in part (c) is unusual because its probability is less than 0.05.
- **O C.** The events in parts (a) and (a) are unusual because their probabilities are less than 0.05.
- **O D.** The event in part (a) is unusual because its probability is less than 0.05.
---
**Additional Information:**
- The time remaining is displayed as 02:49:02.
- A “Next” button appears at the bottom of the screen, suggesting further progression after the current question.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F275f078e-e6df-4549-aae8-3195dc20960c%2F3942f78c-c88d-4951-a4d7-f65655e78edd%2F8gdzawf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image shows a multiple-choice question on evaluating the probability of events in the context of medical student test scores.
---
**Question:**
(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:
- **O A.** None of the events are unusual because all probabilities are greater than 0.05.
- **O B.** The event in part (c) is unusual because its probability is less than 0.05.
- **O C.** The events in parts (a) and (a) are unusual because their probabilities are less than 0.05.
- **O D.** The event in part (a) is unusual because its probability is less than 0.05.
---
**Additional Information:**
- The time remaining is displayed as 02:49:02.
- A “Next” button appears at the bottom of the screen, suggesting further progression after the current question.
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