A comprehensive study of orphaned children is conducted in every orphanage in Australia. A scale called the Capacity for Attachment Scale is given to all orphaned children. The mean (μ) of the scale is 72 and the standard deviation (σ) is 13.
Assuming that the scores are normally distributed, what PERCENTAGE of the population falls between 90 and 63?
Dany/Alicia -- please use the same name for your posts.
sorry me and a group are studying together and we all have similar questions and we can't figure out the answers
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability between the two Z scores. Multiply by 100.
To find the percentage of the population that falls between 90 and 63 on the Capacity for Attachment Scale, we need to calculate the z-scores corresponding to these values and then use a standard normal distribution table.
First, we calculate the z-score for each value using the formula:
z = (x - μ) / σ
Where:
x = the value we want to find the z-score for
μ = the mean of the distribution (72 in this case)
σ = the standard deviation of the distribution (13 in this case)
For 90:
z = (90 - 72) / 13 = 1.38
For 63:
z = (63 - 72) / 13 = -0.69
Now that we have the z-scores, we can use a standard normal distribution table or a statistical software to find the proportion of the population between these z-scores.
Using a standard normal distribution table, we can find the area to the left of each z-score:
For 90: Area to the left of 1.38 = 0.9162
For 63: Area to the left of -0.69 = 0.2454
To find the percentage between 90 and 63, we subtract the smaller area from the larger area:
Percentage = (0.9162 - 0.2454) * 100 ≈ 67.08%
Therefore, approximately 67.08% of the population falls between 90 and 63 on the Capacity for Attachment Scale.