Question

a particular standardized test has scores that have a mound-shaped distribution with mean equal to 120 and standard deviation equal to 17. tom had a raw score of 161, dick scored at the $95^{th}$ percentile, and harry had a z score of 2.00.
arrange these three students in order of their scores from lowest to highest.

Explanation:

Step1: Calculate Tom's z-score

$z_{\text{Tom}} = \frac{161 - 120}{17} = \frac{41}{17} \approx 2.41$

Step2: Find 95th percentile z-score

For mound-shaped (normal) data, the 95th percentile corresponds to a z-score of approximately $z_{\text{Dick}} \approx 1.645$

Step3: Calculate Harry's raw score

$x_{\text{Harry}} = 120 + (2.00 \times 17) = 120 + 34 = 154$

Step4: Compare all scores

Dick's score: $120 + (1.645 \times 17) \approx 120 + 27.965 = 147.97$; Harry's score = 154; Tom's score = 161

Answer:

Dick, Harry, Tom