Can you help me on 10? **Normal Distribution Problems**1. **Problem 10:** - **Given:** - Mean (μ) = 26 - Standard Deviation (σ) = 2.3 - **Task:** - Find the probability of a score above 29.6.2. **Problem 11:** - **Given:** - Mean (μ) = 100 - Standard Deviation (σ) = 25 - **Task:** - Find the score that separates the top 80% from the bottom 20%.**Explanation for Educational Website:**1. **Understanding Problem 10:** To find the probability of a score above a certain value in a normal distribution, we use the Z-score formula which is given by: \[ Z = \frac{X - \mu}{\sigma} \] where \( X \) is the value for which we are finding the probability, \( \mu \) is the mean, and \( \sigma \) is the standard deviation. - Calculate the Z-score for X = 29.6: \[ Z = \frac{29.6 - 26}{2.3} \approx 1.57 \] - Use the Z-table or a calculator to find the area to the right of Z = 1.57, which gives you the probability of a score above 29.6.2. **Understanding Problem 11:** To find the score that separates the top 80% from the bottom 20%, we need to find the corresponding Z-score for the 20th percentile. - The Z-score for the 20th percentile is approximately -0.84 (from Z-tables or standard normal distribution tables). - Use the Z-score formula in reverse to find X: \[ X = \mu + (Z \times \sigma) \] \[ X = 100 + (-0.84 \times 25) \approx 79 \]By solving such problems, students can gain a better understanding of how the properties of the normal distribution apply in real-world scenarios, enhancing their statistical analysis skills.

Name: Can you help me on 10? **Normal Distribution Problems**1. **Problem 10
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: Can you help me on 10? **Normal Distribution Problems**1. **Problem 10:** - **Given:** - Mean (μ) = 26 - Standard Deviation (σ) = 2.3 - **Task:** - Find the probability of a score above 29.6.2. **Problem 11:** - **Given:** - Mea