Question

Scores on the $A C$ T college entrance exam follow a bell-shaped distribution with mean 18 and standard deviation 6 . Wayne's standardized score on the ACT was $-0.5 .$ What was Wayne's actual ACT score? (a) 5.5 (b) 12 (c) 15 (d) 17.5 (e) 21

Name: Problem 27, Chapter 2: The Practice of Statistics for AP
Uploaded: 2023-03-13T04:49:13-08:00
Duration: 2 min 23 s
Channel: Sanchit Jain
Description: Scores on the A C T college entrance exam follow a bell-shaped distribution with mean 18 and standard deviation 6 . Wayne's standardized score on the ACT was -0.5 . What was Wayne's actual ACT score? (a) 5.5 (b) 12 (c) 15 (d) 17.5 (e) 21

   Scores on the $A C$ T college entrance exam follow a bell-shaped distribution with mean 18 and standard deviation 6 . Wayne's standardized score on the ACT was $-0.5 .$ What was Wayne's actual ACT score?
(a) 5.5
(b) 12
(c) 15
(d) 17.5
(e) 21

The Practice of Statistics for AP

Daren S. Starnes,… 5th Edition

Chapter 2, Problem 27

Instant Answer

Solved by Expert Sanchit Jain

03/13/2023

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Wayne's standardized score on the ACT was $z = -0.5$. Show more…

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Scores on the $A C$ T college entrance exam follow a bell-shaped distribution with mean 18 and standard deviation 6 . Wayne's standardized score on the ACT was $-0.5 .$ What was Wayne's actual ACT score? (a) 5.5 (b) 12 (c) 15 (d) 17.5 (e) 21

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Key Concepts

z-Score

A z-score is a standardized score that indicates how many standard deviations an element is from the mean of the distribution. It is computed using the formula: z = (x - mean) / standard deviation. This concept allows for the conversion between a normally distributed value and its relative position in terms of standard deviations, facilitating comparisons across different normal distributions.

Normal Distribution

A normal distribution, also known as a bell-shaped distribution, is a continuous probability distribution that is symmetric about its mean. It is widely used in statistics because many natural phenomena tend to approximate this form, and its shape is determined by the mean (center) and the standard deviation (spread).

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