Teachers in a medium-sized suburban school district have an average salary of $47,500 per year, with a standard deviation of $4,

Question

3 years ago

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Teachers in a medium-sized suburban school district have an average salary of $47,500 per year, with a standard deviation of $4,

600. After negotiating with the school district, teachers recieve a 5% raise and a one-time $500 bonus. What are the new mean and standard deviation of the teacher's salaries during the year in which they recieve bonus?A. $50,125; $4,960B. $49,875; $4,830C. $49,875; $5,330D. $50,375; $4,830E. $50,375; $5,330

Mathematics

2 answers:

natima [27] · Answer 1 · 2022-04-26T23:24:36+03:00

Answer: $49,875; $4,830C.

Step-by-step explanation:

The average salary of Teachers in a medium-sized suburban school district is $47,500 per year.

The standard deviation is $4,600

After negotiating with the school district, teachers recieve a 5% raise and a one-time $500 bonus. The bonus of $500 will not alter the mean and standard deviation because equal amount is added for each teacher.

5% increase in each teacher's salary would differ. Therefore, it will affect the mean and standard deviation by 5%. Therefore, the new mean would be

47500 + (5/100 × 47500) = $49875

The new standard deviation would be

4600 + (5/100 × 4600) = $4830