In a large section of a statistics class, the points for the final exam are normally distributed, with a mean of 74 and a standard deviation of 8. Grades are assigned such that the top 10% receive A's, the next 20% received B's, the middle 40% receive C's, the next 20% receive D's, and the bottom 10% receive F's. Find the lowest score on the final exam that would qualify a student for an A, a B, a C, and a D.The lowest score that would qualify a student for an A is nothing.(Round up to the nearest integer as needed.)The lowest score that would qualify a student for a B is nothing.(Round up to the nearest integer as needed.)The lowest score that would qualify a student for a C is nothing.(Round up to the nearest integer as needed.)The lowest score that would qualify a student for a D is nothing.(Round up to the nearest integer as needed.) ### Standard Normal Distribution Table (Page 2)This table represents the cumulative probability of the standard normal distribution, which is a continuous probability distribution with a mean of 0 and a standard deviation of 1. The z-scores are the values along the leftmost column and top row. The table values represent the probability that a standard normal random variable will be less than or equal to the corresponding z-score.#### Reading the Table- **Row Label (z):** The integer and first decimal point of the z-score.- **Column Label (z):** The second decimal place of the z-score.To find the probability for a z-score:1. Locate the z-score using its first two digits in the leftmost column.2. Use the topmost row for the second decimal place.3. The corresponding value in the table is the cumulative probability.For example, to find $ P(Z \leq 0.56) $:- First, find 0.5 in the z column.- Then, move to column 0.06.- The intersection of row 0.5 and column 0.06 gives 0.7123.#### Table Data:- **z = 0.0 to 0.9**: Provides the probabilities for a z-score ranging from 0.00 to 0.09 and continues incrementally through 0.90.- **z = 1.0 to 2.1**: Continues for z-scores from 1.00 to 2.09.For each z-score, the table cell contains the cumulative probability from negative infinity to that z-score.This standard normal distribution table is a crucial tool in statistical analysis for hypothesis testing and confidence interval estimation. By understanding and utilizing this table, users can determine the probability of events within a normal distribution. **Standard Normal Table (Page 1)**A Standard Normal Table is used in statistics to find the probability that a statistic is observed below a standard normal score (z-score), or between two scores. Here is a portion of the standard normal distribution table covering z-scores from -3.4 to -1.3.| **z** | **0.00** | **0.01** | **0.02** | **0.03** | **0.04** | **0.05** | **0.06** | **0.07** | **0.08** | **0.09** ||--------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|| **-3.4** | 0.0003 | 0.0003 | 0.0003 | 0.0003 | 0.0003 | 0.0003 | 0.0003 | 0.0003 | 0.0003 | 0.0002 || **-3.3** | 0.0005 | 0.0005 | 0.0005 | 0.0005 | 0.0005 | 0.0005 | 0.0005 | 0.0004 | 0.0004 | 0.0004 || **-3.2** | 0.0007 | 0.0007 | 0.0007 | 0.0006 | 0.0006 | 0.0006 | 0.0006 | 0.0006 | 0.0005 | 0.0005 || **-3.1** | 0.0010 | 0.0009 | 0.0009 | 0.0009 | 0.0009 | 0.0008 | 0.0008 | 0.0008 | 0.0007 | 0.0007 || **-3.0** | 0.0013 | 0.0013 |

Name: In a large section of a statistics class, the points for the final ex
Uploaded: 2024-03-20T07:07:12.000Z
Channel: Bartleby
Description: In a large section of a statistics class, the points for the final exam are normally distributed, with a mean of 74 and a standard deviation of 8. Grades are assigned such that the top 10% receive A's, the next 20% received B's, the middle 40%

Answered: In a large section of a statistics…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Topic Video

Question

In a large section of a statistics class, the points for the final exam are normally distributed, with a mean of 74 and a standard deviation of 8. Grades are assigned such that the top 10% receive A's, the next 20% received B's, the middle 40% receive C's, the next 20% receive D's, and the bottom 10% receive F's. Find the lowest score on the final exam that would qualify a student for an A, a B, a C, and a D. The lowest score that would qualify a student for an A is nothing. (Round up to the nearest integer as needed.) The lowest score that would qualify a student for a B is nothing. (Round up to the nearest integer as needed.) The lowest score that would qualify a student for a C is nothing. (Round up to the nearest integer as needed.) The lowest score that would qualify a student for a D is nothing. (Round up to the nearest integer as needed.)

### Standard Normal Distribution Table (Page 2)

This table represents the cumulative probability of the standard normal distribution, which is a continuous probability distribution with a mean of 0 and a standard deviation of 1. The z-scores are the values along the leftmost column and top row. The table values represent the probability that a standard normal random variable will be less than or equal to the corresponding z-score.

#### Reading the Table

- **Row Label (z):** The integer and first decimal point of the z-score.
- **Column Label (z):** The second decimal place of the z-score.

To find the probability for a z-score:
1. Locate the z-score using its first two digits in the leftmost column.
2. Use the topmost row for the second decimal place.
3. The corresponding value in the table is the cumulative probability.

For example, to find $ P(Z \leq 0.56) $:
- First, find 0.5 in the z column.
- Then, move to column 0.06.
- The intersection of row 0.5 and column 0.06 gives 0.7123.

#### Table Data:

- **z = 0.0 to 0.9**: Provides the probabilities for a z-score ranging from 0.00 to 0.09 and continues incrementally through 0.90.
- **z = 1.0 to 2.1**: Continues for z-scores from 1.00 to 2.09.

For each z-score, the table cell contains the cumulative probability from negative infinity to that z-score.

This standard normal distribution table is a crucial tool in statistical analysis for hypothesis testing and confidence interval estimation. By understanding and utilizing this table, users can determine the probability of events within a normal distribution.

**Standard Normal Table (Page 1)**

A Standard Normal Table is used in statistics to find the probability that a statistic is observed below a standard normal score (z-score), or between two scores. Here is a portion of the standard normal distribution table covering z-scores from -3.4 to -1.3.

| **z** | **0.00** | **0.01** | **0.02** | **0.03** | **0.04** | **0.05** | **0.06** | **0.07** | **0.08** | **0.09** |
|--------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|
| **-3.4** | 0.0003 | 0.0003 | 0.0003 | 0.0003 | 0.0003 | 0.0003 | 0.0003 | 0.0003 | 0.0003 | 0.0002 |
| **-3.3** | 0.0005 | 0.0005 | 0.0005 | 0.0005 | 0.0005 | 0.0005 | 0.0005 | 0.0004 | 0.0004 | 0.0004 |
| **-3.2** | 0.0007 | 0.0007 | 0.0007 | 0.0006 | 0.0006 | 0.0006 | 0.0006 | 0.0006 | 0.0005 | 0.0005 |
| **-3.1** | 0.0010 | 0.0009 | 0.0009 | 0.0009 | 0.0009 | 0.0008 | 0.0008 | 0.0008 | 0.0007 | 0.0007 |
| **-3.0** | 0.0013 | 0.0013 |

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Expert Solution

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Hypothesis Tests and Confidence Intervals for Means$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.