#13 ### Statistics and Probability Exercise#### Problem 11**Question:**Suppose that IQ scores have a bell-shaped distribution with a mean of 105 and a standard deviation of 15. Using the empirical rule, what percentage of IQ scores are greater than 120? Please do not round your answer.**Solution:**First, calculate the Z-score for 120 using the formula:\[ Z = \frac{X - \mu}{\sigma} \]where \( X = 120 \), \( \mu = 105 \), and \( \sigma = 15 \):\[ Z = \frac{120 - 105}{15} = 1 \]Next, we find the probability that \( Z \) is greater than 1. Using the empirical rule, the probability that a score is greater than 1 standard deviation above the mean is approximately 15.86553%.**Answer:** \[ 15.86553 \% \]#### Problem 12**Question:**Given the following data, find the weight that represents the 31st percentile.**Data:** Weights of Newborn Babies (in pounds):| 7.9 | 7.6 | 6.5 | 7.9 | 7.4 ||----|----|----|----|----|| 8.5 | 6.2 | 6.9 | 9.2 | 7.8 || 7.4 | 7.0 | 6.5 | 7.9 | 8.2 |**Solution:**Ordering the weights from smallest to largest and finding the 31st percentile involves calculation:\[ 31\% \times 21 = 6.51 \approx 7^{th} \text{ value in the ordered list} \]The ordered list is:\[ 6.2, 6.5, 6.5, 6.9, 7.0, 7.4, 7.4, 7.6, 7.8, 7.9, 7.9, 7.9, 7.9, 8.2, 8.5, 9.2 \]Therefore, the 7th value (which represents the 31st percentile) is:\[ 6.9 \]**Answer:**\[ 6.9 \]

Name: #13 ### Statistics and Probability Exercise#### Problem 11**Question:*
Uploaded: 2024-03-05T11:52:21.000Z
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Description: #13 ### Statistics and Probability Exercise#### Problem 11**Question:**Suppose that IQ scores have a bell-shaped distribution with a mean of 105 and a standard deviation of 15. Using the empirical rule, what percentage of IQ scores are greater than 1