The reading speed of sixth-grade students is normal, with a mean speed of 125 words per minute and a standard deviation of 24 words per minute. Note: For parts (a)-(d), round your answer to 4 decimal places. For part (e), round your answer to nearest whole number. (a) What is the probability that a randomly selected sixth-grade student reads less than 105 words per minute? (b) What is the probability that a randomly selected sixth-grade student reads more than 145 words per minute? (c) What is the probability that a randomly selected sixth-grade student reads between 105 and 135 words per minute?
The reading speed of sixth-grade students is normal, with a mean speed of 125 words per minute and a standard deviation of 24 words per minute. Note: For parts (a)-(d), round your answer to 4 decimal places. For part (e), round your answer to nearest whole number. (a) What is the probability that a randomly selected sixth-grade student reads less than 105 words per minute? (b) What is the probability that a randomly selected sixth-grade student reads more than 145 words per minute? (c) What is the probability that a randomly selected sixth-grade student reads between 105 and 135 words per minute?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Problem 1P
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![### Reading Speed Analysis of Sixth Grade Students
The reading speed of sixth-grade students is normal, with a mean speed of 125 words per minute and a standard deviation of 24 words per minute.
**Note:**
- For parts (a)-(d), round your answer to 4 decimal places.
- For part (e), round your answer to the nearest whole number.
---
#### Problems:
**(a)** What is the probability that a randomly selected sixth-grade student reads less than 105 words per minute?
> [Input box for answer]
**(b)** What is the probability that a randomly selected sixth-grade student reads more than 145 words per minute?
> [Input box for answer]
**(c)** What is the probability that a randomly selected sixth-grade student reads between 105 and 135 words per minute?
> [Input box for answer]
**(d)** Would it be unusual for a sixth-grader to read more than 190 words per minute?
> [Input box for answer] (yes, no)
**(e)** What is the reading speed of a sixth-grader whose reading speed is at the 95th percentile?
> [Input box for answer]
---
**Instructions:**
To solve these problems, you will need to use the properties of the normal distribution. You may use z-scores and standard normal distribution tables or a calculator to find the required probabilities and values.
For example:
- To find the probability in (a), calculate the z-score for 105 words per minute and use the standard normal distribution to find the corresponding probability.
- For part (e), determine the z-score that corresponds to the 95th percentile and use the mean and standard deviation to find the reading speed.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd2297071-c636-4616-baf3-32dd51d4726a%2F2f1f0a49-c881-4bc1-b35b-42c5e8a7b46a%2Fggiz3j8_processed.png&w=3840&q=75)
Transcribed Image Text:### Reading Speed Analysis of Sixth Grade Students
The reading speed of sixth-grade students is normal, with a mean speed of 125 words per minute and a standard deviation of 24 words per minute.
**Note:**
- For parts (a)-(d), round your answer to 4 decimal places.
- For part (e), round your answer to the nearest whole number.
---
#### Problems:
**(a)** What is the probability that a randomly selected sixth-grade student reads less than 105 words per minute?
> [Input box for answer]
**(b)** What is the probability that a randomly selected sixth-grade student reads more than 145 words per minute?
> [Input box for answer]
**(c)** What is the probability that a randomly selected sixth-grade student reads between 105 and 135 words per minute?
> [Input box for answer]
**(d)** Would it be unusual for a sixth-grader to read more than 190 words per minute?
> [Input box for answer] (yes, no)
**(e)** What is the reading speed of a sixth-grader whose reading speed is at the 95th percentile?
> [Input box for answer]
---
**Instructions:**
To solve these problems, you will need to use the properties of the normal distribution. You may use z-scores and standard normal distribution tables or a calculator to find the required probabilities and values.
For example:
- To find the probability in (a), calculate the z-score for 105 words per minute and use the standard normal distribution to find the corresponding probability.
- For part (e), determine the z-score that corresponds to the 95th percentile and use the mean and standard deviation to find the reading speed.
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