Suppose the scores on your last Algebra 2 test were normally distributed, with a mean of 81% and a standard deviation of 3%. To show you how you compared to your classmates, the teacher did not record your grades as per- centages, instead, she wrote them as z-scores. You look at your paper and see "2.66" written at the top. What was your score as a percentage? Explain how you determined your answer.
Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
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Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
![**Understanding Z-Scores in Your Algebra 2 Test**
Suppose the scores on your last Algebra 2 test were normally distributed, with a mean of 81% and a standard deviation of 3%. To show you how you compared to your classmates, the teacher did not record your grades as percentages; instead, she wrote them as z-scores. You look at your paper and see "2.66" written at the top.
**What was your score as a percentage? Explain how you determined your answer.**
To determine your score as a percentage from the given z-score of 2.66, you can use the following formula that relates the z-score to the mean and the standard deviation:
\[ \text{Z-score} = \frac{\text{Your score} - \text{Mean}}{\text{Standard deviation}} \]
Given:
- Mean (\(\mu\)) = 81%
- Standard deviation (\(\sigma\)) = 3%
- Z-score (z) = 2.66
Rearrange the formula to solve for your score (X):
\[ X = \text{Mean} + (\text{Z-score} \times \text{Standard deviation}) \]
\[ X = 81\% + (2.66 \times 3\%) \]
\[ X = 81\% + 7.98\% \]
\[ X = 88.98\% \]
Therefore, your score as a percentage was 88.98%.
This method helps you understand where your score lies in relation to the average score, showcasing your performance relative to your peers through the use of the z-score.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F81d865ca-ed2c-4f6d-a4cc-7f843242dec1%2Fe2c48576-e1b8-4587-a071-a943c89bee9d%2F8dix9e7_processed.jpeg&w=3840&q=75)
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