The scores on a standardized test are normally distributed with a mean of 110 and standard deviation of 5. What test score is 1.4 standard deviations below the mean?
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.
![Title: Understanding Standard Deviation in Normal Distribution
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The scores on a standardized test are normally distributed with a mean of 110 and a standard deviation of 5.
**Problem Statement:**
What test score is 1.4 standard deviations below the mean?
**Solution:**
To find the test score that is 1.4 standard deviations below the mean, we can use the following formula:
\[ \text{Test Score} = \text{Mean} - (\text{Number of Standard Deviations} \times \text{Standard Deviation}) \]
Given:
- Mean (\(\mu\)) = 110
- Standard Deviation (\(\sigma\)) = 5
- Number of standard deviations below the mean = 1.4
Let's plug in the values into the formula:
\[ \text{Test Score} = 110 - (1.4 \times 5) \]
\[ \text{Test Score} = 110 - 7 \]
\[ \text{Test Score} = 103 \]
So, a test score of 103 is 1.4 standard deviations below the mean.
For further questions, feel free to watch the help video by clicking "Question Help: Video."
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This problem helps students understand how to apply the concept of standard deviation in a normally distributed dataset.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa2daf47f-1d43-4c0e-a218-05866800687b%2F7c1488d1-bbfc-4845-9257-91c61bb13d62%2F19t373e.jpeg&w=3840&q=75)
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