The reading speed of second grade students in a large city is approximately normal, with a mean of 91 words per minute (wpm) and a standard deviation of 10 wpm. Complete parts (a) through (f). a) What is the probability a randomly selected student in the city will read more than 97 words per minute? The probability isO. Round to four decimal places as needed.) nterpret this probability. Select the correct choice below and fill in the answer box within your choice. O A. If 100 different students were chosen from this population, we would expect to read exactly 97 words per minute. O B. If 100 different students were chosen from this population, we would expect to read less than 97 words per minute. OC. If 100 different students were chosen from this population, we would expect to read more than 97 words per minute. b) What is the probability that a random sample of 10 second grade students from the city results in a mean reading rate of more than 97 words per minute? The probability is. Round to four decimal places as needed.) nterpret this probability. Select the correct choice below and fill in the answer box within your choice. O A. If 100 different samples of n=10 students were chosen from this population, we would expect sample(s) to have a sample mean reading rate of exactly 97 words per minute. O B. If 100 different samples of n= 10 students were chosen from this population, we would expect sample(s) to have a sample mean reading rate of less than 97 words per minute. O C. If 100 different samples of n= 10 students were chosen from this population, we would expect sample(s) to have a sample mean reading rate of more than 97 words per minute. c) What is the probability that a random sample of 20 second grade students from the city results in a mean reading rate of more than 97 words per minute? The probability is. Round to four decimal places as needed.) nterpret this probability. Select the correct choice below and fill in the answer box within your choice. O A. If 100 different samples of n=20 students were chosen from this population, we would expect sample(s) to have a sample mean reading rate of less than 97 words per minute. O B. If 100 different samples of n = 20 students were chosen from this population, we would expect sample(s) to have a sample mean reading rate of more than 97 words per minute. O C. If 100 different samples of n=20 students were chosen from this population, we would expect sample(s) to have a sample mean reading rate of exactly 97 words per minute.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Question

1

**Standard Normal Distribution Table (Page 1 & Page 2)**

The standard normal distribution, often represented as a bell curve, shows the distribution of data where most values cluster around a central region. This distribution is symmetric, meaning that the left and right sides around the central point (mean) are mirror images. It is essential for calculating probabilities in statistics.

**Diagram Explanation:**
The diagrams on both pages display a bell curve, representing the standard normal distribution. The curve peaks at the mean, zero, and decreases symmetrically on both sides. The shaded region under the curve illustrates the area corresponding to a specific range of values, denoted by "z". The area represents the probability of a value falling within that range.

**Standard Normal Distribution Table:**

The table provides the area (probability) to the left of a given z-score. It is divided into two pages, with z-scores ranging from -3.4 to 3.9.

**Page 1:**
- Z-scores from -3.4 to -0.3.
- The table is structured with the z-score listed in the first column and corresponding probability values spread across additional columns for decimal adjustments (second decimal place).

**Page 2:**
- Z-scores from 0.0 to 3.9.
- Follows the same structure with z-scores in the first column and a series of probabilities representing different decimal places.

**Usage:**
This table helps determine the probability that a standard normal random variable is less than or equal to a given z-score. For instance, to find the probability of a value less than z = 0.5, locate 0.5 in the row under column 0.00 on the second page for the correct probability (approximately 0.6915).

The standard normal distribution table is a crucial tool in statistics for hypothesis testing, confidence interval creation, and probability calculations.
Transcribed Image Text:**Standard Normal Distribution Table (Page 1 & Page 2)** The standard normal distribution, often represented as a bell curve, shows the distribution of data where most values cluster around a central region. This distribution is symmetric, meaning that the left and right sides around the central point (mean) are mirror images. It is essential for calculating probabilities in statistics. **Diagram Explanation:** The diagrams on both pages display a bell curve, representing the standard normal distribution. The curve peaks at the mean, zero, and decreases symmetrically on both sides. The shaded region under the curve illustrates the area corresponding to a specific range of values, denoted by "z". The area represents the probability of a value falling within that range. **Standard Normal Distribution Table:** The table provides the area (probability) to the left of a given z-score. It is divided into two pages, with z-scores ranging from -3.4 to 3.9. **Page 1:** - Z-scores from -3.4 to -0.3. - The table is structured with the z-score listed in the first column and corresponding probability values spread across additional columns for decimal adjustments (second decimal place). **Page 2:** - Z-scores from 0.0 to 3.9. - Follows the same structure with z-scores in the first column and a series of probabilities representing different decimal places. **Usage:** This table helps determine the probability that a standard normal random variable is less than or equal to a given z-score. For instance, to find the probability of a value less than z = 0.5, locate 0.5 in the row under column 0.00 on the second page for the correct probability (approximately 0.6915). The standard normal distribution table is a crucial tool in statistics for hypothesis testing, confidence interval creation, and probability calculations.
The reading speed of second grade students in a large city is approximately normal, with a mean of 91 words per minute (wpm) and a standard deviation of 10 wpm. Complete parts (a) through (f).

(a) What is the probability a randomly selected student in the city will read more than 97 words per minute?

The probability is [ ].
(Round to four decimal places as needed.)

Interpret this probability. Select the correct choice below and fill in the answer box within your choice.

- A. If 100 different students were chosen from this population, we would expect [ ] to read exactly 97 words per minute.
- B. If 100 different students were chosen from this population, we would expect [ ] to read less than 97 words per minute.
- C. If 100 different students were chosen from this population, we would expect [ ] to read more than 97 words per minute.

(b) What is the probability that a random sample of 10 second grade students from the city results in a mean reading rate of more than 97 words per minute?

The probability is [ ].
(Round to four decimal places as needed.)

Interpret this probability. Select the correct choice below and fill in the answer box within your choice.

- A. If 100 different samples of n = 10 students were chosen from this population, we would expect [ ] sample(s) to have a sample mean reading rate of exactly 97 words per minute.
- B. If 100 different samples of n = 10 students were chosen from this population, we would expect [ ] sample(s) to have a sample mean reading rate of less than 97 words per minute.
- C. If 100 different samples of n = 10 students were chosen from this population, we would expect [ ] sample(s) to have a sample mean reading rate of more than 97 words per minute.

(c) What is the probability that a random sample of 20 second grade students from the city results in a mean reading rate of more than 97 words per minute?

The probability is [ ].
(Round to four decimal places as needed.)

Interpret this probability. Select the correct choice below and fill in the answer box within your choice.

- A. If 100 different samples of n = 20 students were chosen from this population, we would expect [ ] sample(s) to have a sample mean reading rate of less than 97 words per minute
Transcribed Image Text:The reading speed of second grade students in a large city is approximately normal, with a mean of 91 words per minute (wpm) and a standard deviation of 10 wpm. Complete parts (a) through (f). (a) What is the probability a randomly selected student in the city will read more than 97 words per minute? The probability is [ ]. (Round to four decimal places as needed.) Interpret this probability. Select the correct choice below and fill in the answer box within your choice. - A. If 100 different students were chosen from this population, we would expect [ ] to read exactly 97 words per minute. - B. If 100 different students were chosen from this population, we would expect [ ] to read less than 97 words per minute. - C. If 100 different students were chosen from this population, we would expect [ ] to read more than 97 words per minute. (b) What is the probability that a random sample of 10 second grade students from the city results in a mean reading rate of more than 97 words per minute? The probability is [ ]. (Round to four decimal places as needed.) Interpret this probability. Select the correct choice below and fill in the answer box within your choice. - A. If 100 different samples of n = 10 students were chosen from this population, we would expect [ ] sample(s) to have a sample mean reading rate of exactly 97 words per minute. - B. If 100 different samples of n = 10 students were chosen from this population, we would expect [ ] sample(s) to have a sample mean reading rate of less than 97 words per minute. - C. If 100 different samples of n = 10 students were chosen from this population, we would expect [ ] sample(s) to have a sample mean reading rate of more than 97 words per minute. (c) What is the probability that a random sample of 20 second grade students from the city results in a mean reading rate of more than 97 words per minute? The probability is [ ]. (Round to four decimal places as needed.) Interpret this probability. Select the correct choice below and fill in the answer box within your choice. - A. If 100 different samples of n = 20 students were chosen from this population, we would expect [ ] sample(s) to have a sample mean reading rate of less than 97 words per minute
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Since you have posted a question with multiple sub-parts, we will solve first three sub-

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(a)

 

Obtain the probability a randomly selected student in the city will read more than 97 words per minute.

 

The probability a randomly selected student in the city will read more than 97 words per minute is obtained below as follows:

Statistics homework question answer, step 1, image 1

The probability a randomly selected student in the city will read more than 97 words per minute is 0.2743.

 

If the 100 different students were chosen from this population, we would expect 27 to read more than 97 words per minute.

 

Correct option: Option C

 

 

 

 

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