Question
Score on last try: 0.67 of 1 pts . See Details for more.
In a normal distribution, a data value located 1.5 standard deviations below the mean has Standard Score:
In a normal distribution, a data value located 1.7 standard deviations above the mean has Standard Score:
In a normal distribution, the mean has Standard Score:
Question Help:
In a normal distribution, a data value located 1.5 standard deviations below the mean has Standard Score:
In a normal distribution, a data value located 1.7 standard deviations above the mean has Standard Score:
In a normal distribution, the mean has Standard Score:
Question Help:
Ask by Savage Reed. in the United States
Nov 12,2024
Upstudy AI Solution
Tutor-Verified Answer
Answer
A data value 1.5 standard deviations below the mean has
A data value 1.7 standard deviations above the mean has
The mean has
A data value 1.7 standard deviations above the mean has
The mean has
Solution
In a normal distribution, the standard score (or z-score) is calculated using the formula:
where:
-
is the data value, -
is the mean of the distribution, -
is the standard deviation.
- For a data value located 1.5 standard deviations below the mean, the z-score can be calculated as follows:
This is because being below the mean means the z-score will be negative.
- For a data value located 1.7 standard deviations above the mean, the z-score is:
This is already given in your question.
- For the mean of the distribution, the z-score is:
This is because the mean is the reference point in the z-score calculation.
So, to summarize:
- A data value located 1.5 standard deviations below the mean has a standard score of
. - A data value located 1.7 standard deviations above the mean has a standard score of
. - The mean has a standard score of
.
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution The Deep Dive
In the realm of normal distributions, the Standard Score, also called the z-score, helps us understand how far a data point is from the mean in terms of standard deviations. For instance, a value that is 1.5 standard deviations below the mean would have a z-score of
Now, let’s take the z-score of a value that’s 1.7 standard deviations above the mean. As you mentioned, this is simply
