One year Perry had the lowest ERA (earned-run average, mean number of runs yielded per nine innings pitched) of any male pitcher at his school, with an ERA of 2.83. Also, Karla had the lowest ERA of any female pitcher at the school with an ERA of 3.37. For the males, the mean ERA was 3.771 and the standard deviation was 0.861. For the females, the mean ERA was 4.979 and the standard deviation was 0.508. Find their respective z-scores. Which player had the better year relative to their peers, Perry or Karla? (Note: In general, the lower the ERA, the better the pitcher.) Perry had an ERA with a z-score of Karla had an ERA with a z-score of (Round to two decimal places as needed.)

The scores on a psychology exam were normally distributed with a mean of 65 and a standard deviation of 6. A failing grade on the exam was anything 2 or more standard deviations below the mean. What was the cutoff for a failing​ score? Approximately what percentage of the students​ failed?

For a social club, the members had a mean age of 68 and a standard deviation of 10 years.  What is the z-score for an age of 50?

In one town, the number of pounds of sugar consumed per person per year has a mean of 6 pounds and a standard deviation of 1.5 pounds. Tyler consumed 10.5 pounds of sugar last year. What percentage of people in the town consumed less sugar than tyler?

Three potential employees took an aptitude test. Each person took a different version of the test. The scores are reported below. Pierce got a score of 71.5; this version has a mean of 62.5 and a standard deviation of 15. Vincent got a score of 309.2; this version has a mean of 294 and a standard deviation of 19. Norma got a score of 7.96; this version has a mean of 7.2 and a standard deviation of 0.4. If the company has only one position to fill and prefers to fill it with the applicant who performed best on the aptitude test, which of applicants should be offered the job?

In one town, the number of pounds of leafy greens consumed per person per year has a mean of 10 pounds and a standard deviation of 2.6 pounds. Tyler consumed 24 pounds of leafy greens last year. How many standard deviations from the mean is that?   a. 5.38 standard deviations below the mean   b. 2.33 standard deviations above the mean   c. 2.33 standard deviations below the mean   d. 5.38 standard deviations above the mean 2. Sue is interested in how many hours U.S. Senators sleep each night. She sends a survey to which all senators respond. Sues’ resulting standard deviation would be denoted as:   a. s because she has obtained a population   b. s because she has obtained a sample   c. s2 because she has obtained a population   d. σ because she has obtained a population   e. σ because she has obtained a sample   f. s2 because she has obtained a sample 3. Determine which of the four levels of measurement is most appropriate for the…

Tanya takes her Physics test and is told that her Z-score is 3.10. If the class mean was 75 and the standard deviation 5, what was Tanya's raw score?

Use z scores to compare the given values.   The tallest living man at one time had a height of 225 cm. The shortest living man at that time had a height of 136.8 cm. Heights of men at that time had a mean of 173.31 cm and a standard deviation of 5.54 cm. Which of these two men had the height that was more​ extreme?

The mean score on the SAT in 2017 was 1060, and the standard deviation was 195. Assume the scores were normally distributed. Suppose someone receives a score of 835. What percentage of the students taking the SAT scored worse?

Abby's score of 704 on the math portion of the 2002 GRE exam placed her in the 84th percentile rank. The standard deviation of this exam was 141. If the test scores are normally distributed, what was the mean score of the 2002 test takers? write your answer with one decimal place.