A man who moves to a new city sees that there are two routes he could take to work. A neighbor who has lived there a long time tells him Route A will average 5 minutes faster than Route B. The man decides to experiment. Each day he flips a coin to determine which way to​ go, driving each route 10days. He finds that Route A takes an average of 50 ​minutes, with standard deviation 1 minute​, and Route B takes an average of 52 ​minutes, with standard deviation 4 minutes. Histograms of travel times for the routes are roughly symmetric and show no outliers.

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A man who moves to a new city sees that there are two routes he could take to work. A neighbor who has lived there a long time tells him Route A will average 5 minutes faster than Route B. The man decides to experiment. Each day he flips a coin to determine which way to​ go, driving each route 10days. He finds that Route A takes an average of
50 ​minutes, with standard deviation 1 minute​, and Route B takes an average of 52 ​minutes, with standard deviation
4 minutes. Histograms of travel times for the routes are roughly symmetric and show no outliers. 
 
​a) Find a​ 95% confidence interval for the difference between the Route B and Route A commuting​ times,
μB−μA.
 
The confidence interval is
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