Question

on a standardized test the scores are normally distributed with a z-score of 3.5 and the standard leave deviation of 18 find the mean for the test if a student scored 230 on the exam.​

Answer 1

To find the mean (μ) for a test where a student scored 230 with a z-score of 3.5 and a standard deviation (σ) of 18, we rearrange the score calculation formula: μ = 230 - (3.5)(18), which gives us a mean of 167.

Step-by-step explanation:

To find the mean of the test scores when a student scored 230 with a z-score of 3.5 given the standard deviation is 18, we use the formula for calculating a score from a z-score:

x = μ + (z)(σ)

Where:

• x is the raw score
• μ is the mean
• z is the z-score
• σ is the standard deviation

We rearrange the formula to solve for the mean (μ):

μ = x - (z)(σ)

Substituting the given values:

μ = 230 - (3.5)(18)

μ = 230 - 63

μ = 167

The mean for the test is 167.