The college physical education department offered an advanced first aid course last semester. The scores on the comprehensive final exam were normally distributed, and the z scores for some of the students are shown below: Robert, 1.10 Juan, 1.70 Susan, −2.00 Joel, 0.00 Jan, −0.80 Linda, 1.60 Which of these students scored above the mean? Which of these students scored on the mean? Which of these students scored below the mean? If the mean score was 50 with standard deviation 20, what was the final exam score for Robert , Joel and Susan ?
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
The college physical education department offered an advanced first aid course last semester. The scores on the comprehensive final exam were
|
Robert, 1.10 |
Juan, 1.70 |
Susan, −2.00 |
|
Joel, 0.00 |
Jan, −0.80 |
Linda, 1.60 |
- Which of these students scored above the
mean ? - Which of these students scored on the mean?
- Which of these students scored below the mean?
- If the mean score was 50 with standard deviation 20, what was the final exam score for Robert , Joel and Susan ?
Given Information:
The scores on the comprehensive final exam were normally distributed, and the z scores for some of the students are as follows:
Robert : 1.10
Juan : 1.70
Susan : -2.00
Joel : 0.00
Jan : -0.80
Linda : 1.60
z-score is a measure which indicates how many standard deviations away, a data value is, from the mean.
It is given by the formula:
A positive z-score means that the data value is above the mean.
A negative z-score means that the data value is below the mean.
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