**Understanding Z-Scores with Commuting Times**Consider the population of commuting time to school for all John Jay College students during Spring 2022. The commuting times have a mean of 95 minutes and a standard deviation of 22 minutes. One student from STA 250-99 class had a commuting time of 2 hours and 15 minutes. What is the z score for this commuting time? (Give your answer correct to two decimal places.)---### Analysis and Explanation:#### Definitions:1. **Mean (μ):** The average value of all the commuting times, which is 95 minutes.2. **Standard Deviation (σ):** A measure of how spread out the numbers are, which is 22 minutes.3. **Z-Score:** The number of standard deviations a data point is from the mean.#### Calculation Steps:1. **Convert the commuting time to minutes**: - 2 hours and 15 minutes = 2 * 60 + 15 = 120 + 15 = 135 minutes.2. **Apply the Z-Score formula**: \[ Z = \frac{(X - \mu)}{\sigma} \] Where: - $ X $ = observed value (135 minutes) - $ \mu $ = mean (95 minutes) - $ \sigma $ = standard deviation (22 minutes)3. **Substitute the values**: \[ Z = \frac{(135 - 95)}{22} \]4. **Calculate the Z-Score**: \[ Z = \frac{40}{22} \approx 1.82 \]#### Conclusion:The z score for the student's commuting time is approximately 1.82. This means the student's commuting time is 1.82 standard deviations above the mean commuting time.---**Note:** Z-Scores allow us to understand how a particular value compares to the overall distribution of the data. In this case, the student's commuting time is significantly above average.

Answered: Image /qna-images/answer/9080a7c3-e2e0-4226-bbc5-5026d347e7a0.jpg

Answered: Consider the population of commuting…

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

Pyramid Lake is on the Paiute Indian Reservation in Nevada. The lake is famous for cutthroat trout. Suppose a friend tells you that the average length of trout caught in Pyramid Lake is ? = 19 inches. However, a survey reported that of a random sample of 46 fish caught, the mean length was x = 18.4 inches, with estimated standard deviation s = 2.7 inches. Do these data indicate that the average length of a trout caught in Pyramid Lake is less than ? = 19 inches? Use ? = 0.05. Solve the problem using the critical region method of testing (i.e., traditional method). (Round the your answers to three decimal places.) test statistic = critical value = State your conclusion in the context of the application. Reject the null hypothesis, there is sufficient evidence that the average fish length is less than 19 inches.Reject the null hypothesis, there is insufficient evidence that the average fish length is less than 19 inches. Fail to reject the null hypothesis, there is…
Suppose SAT Writing scores are normally distributed with a mean of 488 and a standard deviation of 113. A university plans to award scholarships to students whose scores are in the top 10%. What is the minimum score required for the scholarship? Round your answer to the nearest whole number, if necessary.
Pyramid Lake is on the Paiute Indian Reservation in Nevada. The lake is famous for cutthroat trout. Suppose a friend tells you that the average length of trout caught in Pyramid Lake is ? = 19 inches. However, a survey reported that of a random sample of 51 fish caught, the mean length was x = 18.6 inches, with estimated standard deviation s = 3.1 inches. Do these data indicate that the average length of a trout caught in Pyramid Lake is less than ? = 19 inches? Use ? = 0.05. a) Estimate the P-value. select one:P-value > 0.0100.0010 < P-value < 0.010 0.250 < P-value < 0.00100.125 < P-value < 0.250P-value < 0.125 b) Sketch the sampling distribution and show the area corresponding to the P-value. c) will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ??At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the ? = 0.05 level, we reject the null hypothesis and…
College Professors have incomes with a standard deviation that is less than $21,000. A recent study of 225 College Professors income showed a standard deviation of $24,750. State whether it is Right Tail (one), Left Tail (one), In between, or Two tailed?
A successful basketball player has a height of 6 feet 11 inches, or 211 cm. Based on statistics from a data set, his height converts to the z score of 5.17. How many standard deviations is his height above the mean?
Pyramid Lake is on the Paiute Indian Reservation in Nevada. The lake is famous for cutthroat trout. Suppose a friend tells you that the average length of trout caught in Pyramid Lake is ? = 19 inches. However, a survey reported that of a random sample of 51 fish caught, the mean length was x = 18.6 inches, with estimated standard deviation s = 3.5 inches. Do these data indicate that the average length of a trout caught in Pyramid Lake is less than ? = 19 inches? Use ? = 0.05. (a)What is the level of significance? =__ State the null and alternate hypotheses. A-H0: ? = 19 in; H1: ? ≠ 19 in B-H0: ? < 19 in; H1: ? = 19 in C-H0: ? = 19 in; H1: ? < 19 in D-H0: ? = 19 in; H1: ? > 19 in E-H0: ? > 19 in; H1: ? = 19 in (b)What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. A-The Student's t, since the sample size is large and ? is known. B-The standard normal, since the sample size is large and ? is known. C-The…
Imagine that for those who meditate daily, the number of minutes in meditation has mean 35 and standard deviation 10. In a group of 200 such persons, how many are expected to meditate more than 43 minutes per day? Click the icon to view the table of z-scores. Of the 200 persons, approximately will meditate more than 43 minutes per day. (Round to the nearest whole number as needed.)
Consider the following data of 10 exams scores: 28, 57, 58, 64, 69, 74, 79, 80, 83, 85 1. The the mean, median, and mode 2. find the standard deviation without a graphing calculator. Show all your computations
The SAT and ACT college entrance exam are taken by thousands of students each year. The mathematics portions of each of these exams produce scores that are approximately normally distributed. In recent years, SAT mathematics exam scores have averaged 480 with standard deviation 100. The average and standard deviation for ACT mathematics scores are 18 and 6, respectively. a. An engineering school sets 550 as the minimum SAT math score for new students. What percentage of students will score below 550 in a typical year? b. What score should the engineering school set as a comparable standard on the ACT math test?
Suppose scores on an examination are normally distributed. If the examination scores have a mean 60% and a standard deviation of 15%, what is the probability that a student who takes the examination will score between 80% and 90%? I need answer ASAP. Thank you!
A pupil in grade 2 jumped 3.2 m for the long jump. The class mean is 2.5 m with a standard deviation of 0.4 m. A pupil in grade 8 at the same school jumped 4.3 m in a class with a mean of 3.4 m and a standard deviation of 0.5 m. Which student should receive the long jump medal for the school track meet?

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