What raw score marks the cut off score for the children in the 30th percentile (in the bottome 30%) in need of special assistance prior to attending school?
Mean is 30.9, SD = 2.08, N= 20
To determine the raw score cutoff for the children in the 30th percentile, you can use the z-score formula. The z-score measures the number of standard deviations a particular value is from the mean.
First, you need to find the z-score corresponding to the 30th percentile. Since the mean is 30.9 and the standard deviation is 2.08, you can use the z-score formula:
z = (x - mean) / standard deviation
To find the raw score, you rearrange the formula as:
x = (z * standard deviation) + mean
To find the z-score corresponding to the 30th percentile, you can use a standard normal distribution table or a calculator.
Using the standard normal distribution table, the z-score corresponding to the 30th percentile is approximately -0.52.
Now you can substitute the values into the rearranged formula to find the raw score cutoff:
x = (-0.52 * 2.08) + 30.9
x = -1.0816 + 30.9
x ≈ 29.8184
Therefore, the raw score cutoff for the children in the 30th percentile is approximately 29.8184.