Both Questions Please!! **Transcription for Educational Website**---**Problem Statement:**Suppose \( x \) has a normal distribution with \( \sigma = 1.9 \). A random sample of size 70 has a sample mean of \( \bar{x} = 20 \).**Question (a): What conditions are necessary for your calculations? (Select all that apply.)**- [ ] \( \sigma \) is unknown- [x] \( \sigma \) is known- [ ] Uniform distribution of \( x \)- [x] Normal distribution of \( x \)**Explanation:** The conditions necessary for the calculations are that the standard deviation \( \sigma \) is known and that the distribution of \( x \) is normal. These are checked in the options provided.**Question (b): Find a 95% confidence interval for \( \mu \). What is the margin of error? (Round your answers to two decimal places.)**- **Lower limit:** [ ]- **Upper limit:** [ ]- **Margin of error:** [ ]**Note:** Values and calculations for the confidence interval lower limit, upper limit, and margin of error require input and computation based on the sample statistics provided.---This problem requires understanding of normal distributions, confidence intervals, and the conditions for inference in statistics. Suppose \( x \) has a normal distribution with \( \sigma = 1.1 \). A random sample of size 10 has a sample mean of \( \bar{x} = 50 \).(a) What conditions are necessary for your calculations? (Select all that apply.)- [x] \( \sigma \) is known- [x] normal distribution of \( x \)- [ ] uniform distribution of \( x \)- [ ] \( \sigma \) is unknown(b) Find a 90% confidence interval for \( \mu \). What is the margin of error? (Round your answers to two decimal places.)- Lower limit: [ ]- Upper limit: [ ]- Margin of error: [ ]

Name: Both Questions Please!! **Transcription for Educational Website**---**
Uploaded: 2024-03-20T07:07:37.000Z
Channel: Bartleby
Description: Both Questions Please!! **Transcription for Educational Website**---**Problem Statement:**Suppose \( x \) has a normal distribution with \( \sigma = 1.9 \). A random sample of size 70 has a sample mean of \( \bar{x} = 20 \).**Question (a): What condi