# Standard Normal Distribution TableThe standard normal distribution table is a mathematical table commonly used to find the probability that a statistic is observed below, above, or between values on the standard normal distribution, which is a normal distribution with a mean of 0 and a standard deviation of 1. The table is important when performing statistical hypothesis testing.## DiagramsEach page of the table displays a bell curve (normal distribution curve) graphically representing how the values in the table are distributed. The area under the curve to the left of a given z-score represents the cumulative probability of obtaining that score or less.### Page 1#### z-scores ranging from -3.4 to -0.1Each cell within the table shows the probability (area under the curve) associated with the corresponding z-score, which is a measure of how many standard deviations an element is from the mean.- **Vertical Column**: Represents the z-scores in increments of 0.1, starting from -3.4 to -0.1.- **Horizontal Row**: The top row shows increments of 0.01, adding this to the z-score from the vertical column. For example, to find the cumulative probability for a z-score of -1.23, you would find -1.2 in the column and move across to the 0.03 column to get 0.1093.### Page 2#### z-scores ranging from 0.0 to 3.4- **Vertical Column**: Represents z-scores in increments of 0.1, starting from 0.0 to 3.4.- **Horizontal Row**: Similar to page 1, the top row indicates increments of 0.01. For instance, a z-score of 0.57 would be found by locating 0.5 in the vertical column and moving to the 0.07 column, resulting in a cumulative probability of 0.7157.### UsageThese tables are essential in determining probabilities for normally distributed data, making them indispensable for statistical analysis, hypothesis testing, and various fields that require probabilistic evaluation. **Automotive Service Time Analysis**The time required for an automotive center to complete an oil change service on an automobile approximately follows a normal distribution, with a mean of 17 minutes and a standard deviation of 4 minutes.### Tasks**(a)** The automotive center guarantees customers that the service will take no longer than 20 minutes. If it does take longer, the customer will receive the service for half-price. What percent of customers receive the service for half-price? - **Answer**: The percent of customers that receive the service for half-price is [ ]%. (Round to two decimal places as needed.)**(b)** If the automotive center does not want to give the discount to more than 3% of its customers, how long should it make the guaranteed time limit?- **Answer**: The guaranteed time limit is [ ] minutes. (Round up to the nearest minute.)### Additional Resources- Click here to view the standard normal distribution table (page 1).- Click here to view the standard normal distribution table (page 2). The tables provided are necessary for determining the exact percentages and time limits, utilizing the properties of the normal distribution curve. The analysis involves calculating the area under the normal distribution curve for specific conditions outlined in the tasks.

Answered: Image /qna-images/answer/17c7dbee-418a-41c4-91df-5624ad416d20.jpg

Answered: The time required for an automotive…

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

Similar questions

If the mean snowfall for Ottawa Ontario Canada is 98 inches per year and the standard deviation is 25 inches what percentage of the time does Ottawa receive less than 125 inches of snow?
Suppose that the quarterly sales levels among health care information systems companies are approximately normally distributed with a mean of 12 million dollars and a standard deviation of 1.3 million dollars. One health care information systems company considers a quarter a "failure" if its sales level that quarter is in the bottom 20% of all quarterly sales levels. Determine the sales level (in millions of dollars) that is the cutoff between quarters that are considered "failures" by that company and quarters that are not. Carry your intermediate computations to at least four decimal places. Round your answer to one decimal place. million dollars X S
Suppose the exam average in a class is 55% with a standard deviation of 4. What proportion of students scored above 57%? Round to two places.
Suppose that the quarterly sales levels among health care information systems companies are approximately normally distributed with a mean of 9 million dollars and a standard deviation of 1.4 million dollars. One health care information systems company considers a quarter a "failure" if its sales level that quarter is in the bottom 10% of all quarterly sales levels. Determine the sales level (in millions of dollars) that is the cutoff between quarters that are considered "failures" by that company and quarters that are not. Carry your intermediate computations to at least four decimal places. Round your answer to one decimal place.
If a set of observations is normally distributed, what percent of these differ from the mean by (a) more than 2.50? (b) less than 0.640?
A normally distributed data set has a mean of 0 and the standard divitation of 2. What is the percent of valleys between -4.0 and 2.0?
Suppose that the quarterly sales levels among health care information systems companies are approximately normally distributed with a mean of 8 million dollars and a standard deviation of 1.3 million dollars. One health care information systems company considers a quarter a "failure" if its sales level that quarter is in the bottom 10% of all quarterly sales levels. Determine the sales level (in millions of dollars) that is the cutoff between quarters that are considered "failures" by that company and quarters that are not. Carry your intermediate computations to at least four decimal places. Round your answer to one decimal place. 00 0 million dollars X S ? Check acer Q tab esc ! 1 9. a @ 2 W →> S #m 3 X e C d $ LAS 4 C r % 5 f t > < 6 g y & JX b 7 h C n K1300
In Professor Krugman’s economics course, the correlation between the students’ total scores prior to the final examination and their final‑examination scores is ?=0.5.r=0.5. The pre‑exam totals for all students in the course have mean 280280 and standard deviation 40.40. The final‑exam scores have mean 7575 and standard deviation 8.8. Professor Krugman has lost Julie’s ﬁnal exam but knows that her total before the exam was 300.300. He decides to predict her ﬁnal‑exam score from her pre‑exam total. (a) Which of the choices is the least‑squares regression line of ﬁnal‑exam scores on pre‑exam total scores in this course?
If the weight of fertilizer in a 40-pound bag is normally distributed with a standard deviation of 0.5 pounds, what is the range of weights of bags of fertilizer within two standard deviations of the mean?
Suppose that you are designing an instrument panel for a large industrial machine. The machine requires the person using it to reach 2 feet from a particular position. The reach from this position for adult women is known to have a mean of 2.7 feet with a standard deviation of 0.5. The reach for adult men is known to have a mean of 3.1 feet with a standard deviation of 0.7. Both women's and men's reach from this position is normally distributed. If this design is implemented, (a) what percentage of women will not be able to work on this instrument panel? (b) What percentage of men will not be able to work on this instrument panel? (c) Explain your answers to a person who has never had a course in statistics. Click here to view page 1 of the table. Click here to view page 2 of the table. Click here to view page 3 of the table. Click here to view page 4 of the table.

Recommended textbooks for you

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

Elementary Statistics: Picturing the World (7th E…

Statistics

ISBN:

9780134683416

Author:

Ron Larson, Betsy Farber

Publisher:

PEARSON

The Basic Practice of Statistics

Statistics

ISBN:

9781319042578

Author:

David S. Moore, William I. Notz, Michael A. Fligner

Publisher:

W. H. Freeman

Introduction to the Practice of Statistics

Statistics

ISBN:

9781319013387

Author:

David S. Moore, George P. McCabe, Bruce A. Craig

Publisher:

W. H. Freeman

SEE MORE TEXTBOOKS