a math test has a mean of 43 and a standard deviation 0f 17.0. find the corresponding z scores for. show all work.
I. a test score of 13
II. a test score of 59
z = (x - mean)/(standard deviation)
how is the problem worked out?
hey cat:
thank you for the information. so clarify i would just plug in the test scores such as 13 and 59 for the x value and 43 for mean with 17.0 for the standard deviation to come up with the following :
z=(13-43)/17.0= 10.47058824 to round off to 10.0?
z= (59-43)/17.0=56.47058824, round off to ?
please coonfirm and show where i went wrong. thank you very much.
mary
Z=(13-43)/17=-1.76
Z=(59-43)/17=0.94
To find the corresponding z-scores, you need to use the formula:
z = (x - μ) / σ
where:
- x is the value you want to find the z-score for,
- μ is the mean, and
- σ is the standard deviation.
Let's calculate the z-scores for the given test scores:
I. A test score of 13.
Using the formula: z = (x - μ) / σ,
z = (13 - 43) / 17
= -30 / 17
≈ -1.7647
Therefore, the z-score for a test score of 13 is approximately -1.7647.
II. A test score of 59.
Using the formula: z = (x - μ) / σ,
z = (59 - 43) / 17
= 16 / 17
≈ 0.9412
Therefore, the z-score for a test score of 59 is approximately 0.9412.
To calculate the z-score, you subtract the mean from the given value and then divide by the standard deviation. This allows you to standardize the data and determine how many standard deviations away from the mean a particular value is.