Subjects statistics

Z Score Probabilities C91Edb

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1. **State the problem:** Match each Z-score with its corresponding cumulative probability (area under the standard normal curve to the left of the Z-score). 2. **Recall the standard normal distribution properties:** - The mean is 0 and standard deviation is 1. - The cumulative probability for Z=0 is 0.5 because the curve is symmetric. - Use the Z-table to find probabilities for other Z-scores. 3. **Find probabilities for each Z-score:** - For $Z=0$, cumulative probability is $0.5000$. - For $Z=2.00$, from Z-table, cumulative probability is approximately $0.9772$. - For $Z=-0.50$, cumulative probability is approximately $0.3085$. - For $Z=1.5$, cumulative probability is approximately $0.9332$. - For $Z=-1.96$, cumulative probability is approximately $0.0250$. 4. **Summary of matches:** - $Z=0 \rightarrow 0.5000$ - $Z=2.00 \rightarrow 0.9772$ - $Z=-0.50 \rightarrow 0.3085$ - $Z=1.5 \rightarrow 0.9332$ - $Z=-1.96 \rightarrow 0.0250$