Math Problem Solver

a) A school administers two different standardized exams: Math and Science. The results are as follows:

· Math Exam: Mean = 75, Standard Deviation = 8

· Science Exam: Mean = 80, Standard Deviation = 5

· A student scores 85 in Math and 88 in Science.

i. Calculate the Z-score for each subject. (4 Marks)

ii. In which subject did the student perform better relative to their peers? (2 Marks)

(b) Two oil refineries, Refinery A and Refinery B, produce oil and track their daily production output. The statistics for each refinery are as follows:

· Refinery A: Mean daily production = 500,000 barrels, Standard Deviation = 40,000 barrels

· Refinery B: Mean daily production = 450,000 barrels, Standard Deviation = 35,000 barrels

· On a particular day, Refinery A produces 560,000 barrels, and Refinery B produces 500,000 barrels.

i. Calculate the Z-score for each refinery’s production on that day. (4 Marks)

ii. Which refinery had a more exceptional production day relative to its typical performance? (2 Marks)

(c) Two airlines, Airline X and Airline Y, report their on-time arrival percentages for the past 12 months. The data is summarized below:

Airline Mean On-Time Arrival % (μ) Standard Deviation (σ)

X 85% 5%

Y 80% 4%

In a particular month, Airline X achieved an on-time arrival rate of 90%, while Airline Y achieved an on-time arrival rate of 85%.

i. Calculate the z-scores for both airlines' on-time arrival rates for that month. (4 Marks)

ii. Compare the performance of Airline X and Airline Y relative to their historical performance. Which airline performed better, and why? (2 Marks