B. Solve the following worded problems. 1. A call center tracks the number of calls handled per hour. The average is 60 calls with a standard deviation of 5 calls. If a representative has a z-score of 1.4, what was their actual number of calls handled during that hour? Given (3pts) Requirements (1pt) Equation (1pt) Solution (7pts) Answer/Conclusion (3pts) 2. A university records the scores of students on a final Statistics exam. The scores are normally distributed with a mean of 72 and a standard deviation of 10. Find the standard score (z-score) for a student who scored 85 on the exam. Given (3pts) Requirements (1pt) Equation (1pt) Solution (7pts) Answer/Conclusion (3pts)

To solve the given word problems involving z-scores, let's go through them step-by-step.
Problem 1:
Given:

Average number of calls (mean, μ ): 60
Standard deviation ( σ ): 5
Z-score of the representative: 1.4

Requirements:
Find the actual number of calls handled by the representative.
Equation:
To find the actual number of calls handled, use the formula for the z-score: z = σ X − μ ​ Where:

z is the z-score
X is the actual number of calls
μ is the mean
σ is the standard deviation

Solution:
Rearrange the z-score formula to solve for X : X = z × σ + μ Substitute the given values into the equation: X = 1.4 × 5 + 60 = 7 + 60 = 67
Answer/Conclusion:
The representative handled 67 calls during that hour.
Problem 2:
Given:

Mean score ( μ ): 72
Standard deviation ( σ ): 10
Student’s score ( X ): 85

Requirements:
Find the z-score for a student who scored 85.
Equation:
Use the z-score formula: z = σ X − μ ​
Solution:
Substitute the given values into the equation: z = 10 85 − 72 ​ = 10 13 ​ = 1.3
Answer/Conclusion:
The standard score (z-score) for the student who scored 85 is 1.3.

Answered by LiamAlexanderSmith | 2025-07-21