Pregunta
Comparing the relative sizes of data values based on thelr z-scores
Jane and Salma each graduated from college last year and got entry-level positions, Last year, the distributions of entry-level salaries were clearly bell-shaped
for mathematicians and for pharmacists. That year, the entry-level salaries of mathematicians had a population mean of
Last year, Jane got an entry-level position as a mathematician with a salary of
(a) Find the z-scores of Jane’s entry-level salary as a mathematician and Salma’s entry-level salary as a pharmacist. Round
your answers to two decimal places.
z-score of Jane’s salary:
z-score of Salma’s salary:
(b) Relative to her population, who got the higher salary?
Choose the best answer based on the z-scores of the two salaries.
O Jane
O Salma
O It is unclear who got the higher salary relative to her population
(5)
Jane and Salma each graduated from college last year and got entry-level positions, Last year, the distributions of entry-level salaries were clearly bell-shaped
for mathematicians and for pharmacists. That year, the entry-level salaries of mathematicians had a population mean of
Last year, Jane got an entry-level position as a mathematician with a salary of
(a) Find the z-scores of Jane’s entry-level salary as a mathematician and Salma’s entry-level salary as a pharmacist. Round
your answers to two decimal places.
z-score of Jane’s salary:
z-score of Salma’s salary:
(b) Relative to her population, who got the higher salary?
Choose the best answer based on the z-scores of the two salaries.
O Jane
O Salma
O It is unclear who got the higher salary relative to her population
(5)
Ask by Frazier Tran. in the United States
Mar 20,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
Jane’s z-score is 2.37, and Salma’s z-score is -3.66. Therefore, Jane received a higher salary relative to her population.
Solución
Step 1. Compute the z-score of Jane’s salary as a mathematician
The formula for a z-score is given by
where
For Jane,
So, the z-score is
Step 2. Compute the z-score of Salma’s salary as a pharmacist
For Salma,
Thus, her z-score is
Step 3. Compare the z-scores to determine the relative standing
The z-score tells us how many standard deviations the value
- Jane’s z-score is
, which means her salary is standard deviations above the mathematicians’ mean. - Salma’s z-score is
, which means her salary is standard deviations below the pharmacists’ mean.
Since a higher z-score indicates a salary that is farther above the mean relative to the population, Jane’s salary is relatively much higher compared to her population.
Answer
- z-score of Jane’s salary:
- z-score of Salma’s salary:
Relative to her population, Jane got the higher salary.
Respondido por UpStudy AI y revisado por un tutor profesional
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Simplifique esta solución Mind Expander
To find Jane’s z-score, use the formula:
For Jane:
Now for Salma:
So, rounding to two decimal places gives:
z-score of Jane’s salary: 2.37
z-score of Salma’s salary: -3.66
z-score of Jane’s salary: 2.37
z-score of Salma’s salary: -3.66
Now, comparing their z-scores, Jane’s z-score (2.37) is much higher than Salma’s z-score (-3.66). This means relative to their populations, Jane got the higher salary. So the best answer is: Jane.
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