need some help on this please ### Understanding the Normal Distribution: Applying the 68-95-99.7 RuleSuppose a normally distributed set of data has a mean of 150 and a standard deviation of 17. **Use the 68-95-99.7 rule to determine the percent of scores in the data set expected to be between the scores 116 and 167**.To address this, keep in mind the following key points regarding the 68-95-99.7 Rule (Empirical Rule):1. **68% of the data** falls within 1 standard deviation of the mean.2. **95% of the data** falls within 2 standard deviations of the mean.3. **99.7% of the data** falls within 3 standard deviations of the mean.### Example Calculation:- **Mean (\(\mu\))** = 150- **Standard Deviation (\(\sigma\))** = 17Using the formula \( \mu \pm n\sigma \):- **1 standard deviation (\(\mu \pm \sigma\))**: \(150 \pm 17\) which gives (133, 167).- **2 standard deviations (\(\mu \pm 2\sigma\))**: \(150 \pm 2 \times 17\) which gives (116, 184).- **3 standard deviations (\(\mu \pm 3\sigma\))**: \(150 \pm 3 \times 17\) which gives (99, 201).To find the percent of scores between 116 and 167:- 116 is \(2\sigma\) below the mean: \(\mu - 2\sigma\) = \(150 - 34 = 116\)- 167 is \(1\sigma\) above the mean: \(\mu + 1\sigma\) = \(150 + 17 = 167\)**Conclusion:**Using the 68-95-99.7 Rule:- Between \(\mu - 2\sigma\) and \(\mu + \sigma\): which accounts for data from (116) to (167) - This range includes the following: - From \(\mu - 2\sigma\) to \(\mu\) = 95%/2 = 47.5% - From \(\mu\) to \(\mu + \sigma

Name: need some help on this please ### Understanding the Normal Distributio
Uploaded: 2024-03-20T07:06:27.000Z
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Description: need some help on this please ### Understanding the Normal Distribution: Applying the 68-95-99.7 RuleSuppose a normally distributed set of data has a mean of 150 and a standard deviation of 17. **Use the 68-95-99.7 rule to determine the percent of sc