Watch the video version of this Q&A episode on YouTube - https://youtu.be/mSFsi6u3_eE

An eight-month-old child with suspected gross motor delay has a z-score of -1.0 on a norm-referenced test of gross motor ability with a normal distribution. Based on the presented data, what approximate percentage of the sample did the child score better than?

1. 16%
2. 68% 
3. 84%
4. 95%

Transcript

Welcome back to the Scorebuilders’ Question and Answer Podcast! This podcast provides members of the Scorebuilders’ team with the opportunity to explore challenging multiple-choice examination questions with students actively preparing for the licensing examination. My name is Scott Giles and I will be your host for today’s journey.

Ready? Let’s go!

An eight-month-old child with suspected gross motor delay has a z-score of -1.0 on a norm-referenced test of gross motor ability with a normal distribution. Based on the presented data, what approximate percentage of the sample did the child score better than?

1. 16%
2. 68% 
3. 84%
4. 95%

The ability to answer this question will be primarily influenced by your familiarity with characteristics of the normal distribution. Let’s take a deeper dive into this measure. 

Normal Distribution
The normal distribution presents as a bell-shaped curve with the majority of data clustered around the mean. The mean, median, and mode are the same in the normal distribution. 

The normal distribution is very useful for answering questions about probability, because once it is determined how many standard deviations a particular result lies away from the mean, it’s possible to determine the probability of seeing a result greater or less than the result in question.

The figure below shows the percentage of observations that would lie within 1, 2, or 3 standard deviations from any mean obtained from normally distributed data.

• Approximately 68% of all values fall within one standard deviation above and below the mean
  Approximately 95% of all values fall within two standard deviations above and below the mean
• Approximately 99% of all values fall within three standard deviations above and below the mean
• Norm-referenced standardized tests are used frequently in pediatric physical therapy to assess if a child’s gross motor skills are within the established average range for a given age. Several tests use z-scores, although many tests use percentiles which are based on the z-score. 

An eight-month-old child with suspected gross motor delay has a z-score of -1.0 on a norm-referenced test of gross motor ability with a normal distribution. Based on the presented data, what approximate percentage of the sample did the child score better than?

The question indicates that the child has a z-score of -1.0 which is equivalent to one standard deviation below the mean. 

The question is asking what approximate percentage of the sample did the child score better than?

Let’s explore each of the options:

Option 1 - 16%
A z-score of -1.0 is equivalent to one standard deviation below the mean. Based on a normal distribution, this indicates that the child scored better than 16% of the normed sample.

Option 2 - 68% 
68% represents the normed sample that scored between -1.0 and +1.0 below/above the mean. 

Option 3 - 84%
A z-score of -1.0 indicates that the child scored lower than 84% of the normed sample, while a z-score of +1.0 corresponds to the child scoring higher than 84% of the normed sample. The question is asking “What approximate percentage of the sample did the child score better than?” Therefore, the answer to the question is 16% and not 84%. 

Option 4 - 95%
95% represents the normed sample that scored between -2.0 and +2.0 below/above the mean. Children who score below -2.0 standard deviations below the mean often demonstrate a significant gross motor delay. 

The correct answer is Option 1

Let’s explore the all student data:
44% of students selected Option 1, 16%, the correct response
36% of students selected Option 2, 68%
8% of students selected Option 3, 84%
12% of students selected Option 4, 95%

System Classification
This question is a Non-Systems question which represents approximately 14% of all exam items.

Content Outline Classification
This question is a Safety and Protection; Professional Responsibilities; Research question which represents approximately 8% of all exam items.

Level Classification
This question is a Level 1 question since the question requires students to possess basic foundational academic knowledge. Remediation of Level 1 questions occurs through academic review of entry-level content using textbooks, review books, Basecamp, and flash cards.

Academic Focus Area
Looking to review related academic content? Check out pages 839-840 in PTEXAM: The Complete Study Guide.

Thanks for joining us on the Scorebuilders Q and A podcast! See you next week!