Using the z Distribution Transcript
There are five questions in this activity. Answer each question and compare your answer to the sample provided.
The first question is:
IQ scores have a population mean of 100 and standard deviation of 15. A school would like to identify students scoring above 130 for their gifted program. What percent of the population would be expected to have an IQ above 130?
Compare your answer to this sample answer:
2.3% would be expected to have an IQ above 130. To find this value, remember: x->z->%.
First convert the raw score to a z-
score: z = (130-100)/15=2. Then, use either the z-
score Converter or z-
score table to find the percent above 2.3%.
NOTE: z and percentile values may deviate slightly from the values given here, depending on the source.
The second question is:
For male children aged 24 months in the U.S., the average height is 34.35 inches, with a standard deviation of 1.39 (National Center for Health Statistics, 2009). The parents of a 24-
month-old male child, Nolan, want to know how his height of 32 inches compares to the height of other 24-month-old male children. Find Nolan’s percentile.
Compare your answer to the following sample answer:
Nolan’s length is at the 4.6
th
percentile for height. To find this value, remember: x->z->%.
First convert the raw score to a z-
score: z = -1.69. Then, use either the z-
score Converter or z-
score table to find the percent below: 4.6%.
NOTE: z and percentile values may deviate slightly from the values given here, depending on the source.
The third question is:
An instructor knows the mean exam score is 81 points (out of 100 possible points) and the standard deviation is 5.7. The instructor is interested in what percentage of students scored between 70 points (a passing grade) and 90 points (graded as an A-).
Compare your answer to the sample answer:
91.6% of scores are between 70 and 90 points. First you will need to find the z-
scores and percentiles for the raw scores for 70 and 90 points. For a score of 70, z =
(70-81)/5.7 = -1.93; the percentile is 2.7. For a score of 90, z =
(90-81)/5.7 = 1.58; the percentile is 94.3. Last subtract the percentiles: 94.3-2.7 = 91.6.
NOTE: z and percentile values may deviate slightly from the values given here, depending on the source.
The fourth question is:
Second-graders take a reading assessment (population mean = 220, standard deviation = 3) to make sure they are on track to pass the state-mandated third-grade reading test. A school wants to implement an intervention program for students who are scoring at the bottom 10% of the scores. Identify the score that marks the bottom 10% of the distribution.
Compare your answer to the sample answer:
91.6% of the scores are between 70 and 90 points. First you will need to find the z-
scores and percentiles for the raw scores for 70 and 90 points. For a score of 70, z = (70-81)/5.7 = - 1.93; the percentile is 2.7. For a score of 90, z =
(90-81)/ 5.7 = 1.58; the percentile is 94.3. Last subtract the percentiles: 94.3 – 2.7 = 91.6.
NOTE: z and percentile values may deviate slightly from the values given here, depending on the source.
