A random sample of 70 observations produced a mean off x =24.1 from a population with a normal distribution and a standard deviation σ=3.68.
Transcribed Image Text:### Confidence Intervals for Population Mean (µ)
#### (a) 90% Confidence Interval
Find a 90% confidence interval for the population mean (µ):
\[ \text{Lower Bound} \leq \mu \leq \text{Upper Bound} \]
#### (b) 95% Confidence Interval
Find a 95% confidence interval for the population mean (µ):
\[ \text{Lower Bound} \leq \mu \leq \text{Upper Bound} \]
#### (c) 99% Confidence Interval
Find a 99% confidence interval for the population mean (µ):
\[ \text{Lower Bound} \leq \mu \leq \text{Upper Bound} \]
### Explanation
This educational content guides you through finding confidence intervals for a population mean (µ) at different confidence levels. The intervals are represented as inequalities, with a blank space for inputs indicating where the calculated lower and upper bounds should be entered. A higher confidence level corresponds to a wider interval, reflecting greater certainty about the inclusiveness of µ within the specified range.
Transcribed Image Text:A random sample of 70 observations produced a mean of \( \bar{x} = 24.1 \) from a population with a normal distribution and a standard deviation \( \sigma = 3.68 \).
Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.
Expert Solution
Step 1: Determining the given information
The sample size is 70, the sample mean is 24.1 and the population standard deviation is 3.68.
![### Confidence Intervals for Population Mean (µ)
#### (a) 90% Confidence Interval
Find a 90% confidence interval for the population mean (µ):
\[ \text{Lower Bound} \leq \mu \leq \text{Upper Bound} \]
#### (b) 95% Confidence Interval
Find a 95% confidence interval for the population mean (µ):
\[ \text{Lower Bound} \leq \mu \leq \text{Upper Bound} \]
#### (c) 99% Confidence Interval
Find a 99% confidence interval for the population mean (µ):
\[ \text{Lower Bound} \leq \mu \leq \text{Upper Bound} \]
### Explanation
This educational content guides you through finding confidence intervals for a population mean (µ) at different confidence levels. The intervals are represented as inequalities, with a blank space for inputs indicating where the calculated lower and upper bounds should be entered. A higher confidence level corresponds to a wider interval, reflecting greater certainty about the inclusiveness of µ within the specified range.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff71a6399-b1b7-4d60-a35b-aee519cd2d65%2F8ab32271-8dc0-4231-926d-59c5ea879ec0%2Fa24q07o_processed.jpeg&w=3840&q=75)
