Directions: Answer questions 1 through five. Make sure to show all your work of how you arrived at your answers.
1. For a group of 20 students taking the final exam, the mean heart rate was 96 beats per minute, and the standard deviation was 5 . Construct a 95 confidence interval of the true mean ( 20 points)
2. The president of a large university wished to estimate the average age of the students presently enrolled. From past studies the standard deviation is known to be 2 years. A sample of 50 students is selected, and the mean is found to be 23.2 years. Construct a \( 90 \% \) confidence interval for the population mean ( 20 points)
3. A Gallup poll conducted in November 2010 found that 493 of 1050 adult Americans believes it is the responsibility of the federal government to make sure all Americans have healthcare coverage. Construct a \( 99 \% \) confidence interval for the proportion of adult Americans who believe it is the responsibility of the federal government to make sure all Americans healthcare coverage ( 20 points).