Scores on a math test are normally distributed with a mean of 76 and a standard deviation of 6. Part A: Find the probability a student scored between 70 and 58. Round to the nearest hundredth Part B: Find the probability a student scored above a 82. Round to the nearest hundredth
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.
![### Math Test Scores Distribution
Scores on a math test are normally distributed with a mean of 76 and a standard deviation of 6.
#### Probability Calculations:
**Part A:** Find the probability a student scored between 70 and 58. *Round to the nearest hundredth*
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**Part B:** Find the probability a student scored above an 82. *Round to the nearest hundredth*
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This problem involves understanding the normal distribution of data and calculating probabilities based on specific score ranges. Use statistical tools or standard normal distribution tables to find the required probabilities.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F79f12dcc-440e-4ad0-9305-8a1742f3d253%2F87829ddf-60b3-443a-868a-f5801122d482%2Fuxrlvlc_processed.jpeg&w=3840&q=75)

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