What proportion of employees spend less than 15 minutes a day commuting?

Statistical Methods for Psychology
Tarleton State University Exam 1: Spring 2023
Instructions: please complete each problem below. You may submit your completed exam in Canvas
using one of two file formats: either (1) write your solutions on paper and scan to a PDF, or (2) write your solutions in a Word/OpenOffice document. Be sure to save your work as a PDF. On either method, please show (or describe) as much work as possible. Report your final answers rounded to 2 decimal places. I believe in you!
1. A sample of N = 35 scores has a mean of X = 10. One score of X = 51 is added to the sample. What is the new value for the sample mean?
2. An expert reviews a sample of 8 scientific articles and records the following numbers of errors in each article: 2, 5, 6, 9, 4, 6, 3, 7. Compute the mean and median for this data.
3. A social psychologist records the age (in years) that a sample of eight participants experienced coffee for the first time. The recorded ages are 21, 19, 16, 14, 16, 15, 17, 11. Compute the variance and standard deviation for this data.
4. For a set of scores with mean 80 and standard deviation 15, find the z-score that corresponds to each of the following X-values: 55, 65, 35, 20.
5. For a set of scores with μ = 145 and σ = 25, find the X-value that corresponds to each of the following z-scores: 1.50, -0.50, 2.00, -1/3
6. A set of exams are reported as X-values and z-scores. On this exam a score of X = 82 corresponds to a Z = 0.5 and X = 70 corresponds to a Z = 1.0. Use this information to find the mean and standard deviation for the complete set of exams.
7. A set of exam scores has a mean of 50 and a standard deviation of 8. The instructor would like to transform the scores into a standardized distribution with a new mean of 100 and new standard deviation of 15. Find the transformed value for each of the following scores from the original population: 55, 67, 46, 34.
8. A normal distribution has a mean of μ = 85 with σ = 5. What proportion of scores in this distribution are:
(a) Above 115?
(b) Below 118?
(c) Between 91 and 115?
9. The average employee in the US spends μ = 25 minutes commuting to work each day. Assume that the distribution of commute times is normal with a standard deviation of σ = 8 minutes.
(a) What proportion of employees spend less than 15 minutes a day commuting?
(b) What proportion of employees spend more than 30 minutes commuting each day?
Wait! There is one more problem on the next page!
PSYC 2317: Statistical Methods for Psychology
Tarleton State University Exam 1: Spring 2023
10. For a normal population with μ = 50 and σ = 15, what is the probability of obtaining a
sample mean:
(a) Greater than 62 for a sample of n = 36 scores?
(b) Greater than 62 for a sample of n = 9 scores?

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