A 2019 Ipsos poll of 4,000 U.S. adults found that 65% play video games on their computer, gaming console, or smartphone. 

a. Use this sample result and a theory-based approach to produce three confidence intervals (90%, 95%, 99%) for the probability that a randomly selected American adult plays video games on their computer, gaming console, or smartphone. 

b. How do the midpoints of these three intervals compare? 

c. How do the widths of these three intervals compare? Is this what you expected? Explain. 

d. Based on the confidence intervals, does the sample result provide strong evidence that more than 64% of all U.S. adults play video games on their computer, gaming console, or smartphone. Explain. 

e. Is it appropriate to use the theory-based approach to find the confidence intervals? Answer this by stating the validity condition, and explain whether or not the condition is satisfied.