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What is the percentage of people with blood pressure readings above 117

To find the percentage of people with blood pressure readings above 117, we first need to convert the blood pressure reading into a z-score using the given mean and standard deviation. The mean (\(\mu\)) is 120, and the standard deviation (\(\sigma\)) is 10.

The z-score is calculated using the formula:

\[ z = \frac{X - \mu}{\sigma} \]

where \( X \) is the value of the blood pressure reading. Substituting the given values:

\[ z = \frac{117 - 120}{10} = \frac{-3}{10} = -0.3 \]

Next, we use the z-score to find the corresponding percentile. From the provided table, we look for the z-score of -0.3. 

According to the table, a z-score of -0.3 corresponds to a percentile of approximately 38.21. This means that 38.21% of people have blood pressure readings below 117.

To find the percentage of people with readings above 117, we subtract this percentile from 100%:

\[ 100\% - 38.21\% = 61.79\% \]

Therefore, the percentage of people with blood pressure readings above 117 is approximately 61.79%.

Would you like more details or have any other questions?

Here are 5 numbered questions you might consider next:
1. How do you interpret a z-score in a normal distribution?
2. What are the steps to find the percentile given a z-score?
3. How can you use the z-score to compare different datasets?
4. What is the significance of the mean and standard deviation in a dataset?
5. How would you find the probability of a range of values in a normal distribution?

**Tip:** Always double-check the table values for accuracy when converting z-scores to percentiles.

Learn how to calculate the percentage of people with blood pressure readings above 117 using z-scores and the normal distribution. Understand the steps involved in converting blood pressure readings to z-scores, finding percentiles, and interpreting the results. Suitable for advanced high school students and anyone interested in statistics and probability.

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