True or False
For a sample with M = 20 and s = 1, a score of X = 17 would be considered an extremely low score.
So would the answer be false
To determine if a score of X = 17 is considered extremely low, we would need to understand the context of the data. Specifically, we would need to know the distribution of scores in the sample and calculate the Z-score.
A Z-score measures how many standard deviations a particular data point is from the sample mean. It helps us understand how unusual or extreme a score is compared to the rest of the data.
To calculate the Z-score, we need the sample mean (M), standard deviation (s), and the value we are interested in (X = 17). The formula for calculating the Z-score is:
Z = (X - M) / s
Given that M = 20 and s = 1, let's calculate the Z-score for X = 17:
Z = (17 - 20) / 1
Z = -3 / 1
Z = -3
Now let's interpret the Z-score. A Z-score of -3 indicates that the score of 17 is 3 standard deviations below the mean. In a normal distribution, about 99.7% of the data falls within 3 standard deviations from the mean.
Since a Z-score of -3 is very low and falls in the extreme tail of the distribution, we can conclude that a score of X = 17 would indeed be considered an extremely low score in this sample.
Therefore, the answer is True.