please answer in mathematical details with explanation, you can use Excel but plz refer to that in the spreadsheet with formulas , plz also include interpretation for the answer

1- To test a new tread design with respect to stopping distance, a tire manufacturer manufactures a set of 25 prototype tires and measures the stopping distance from 70 mph on a standard test car. Their Operations team reported that, based on this sample, which had a sample standard deviation of 8 feet, the stopping distance is between 169 and 177 feet.

(a) What is the best estimate of the stopping distance for this tread design? (b) How confident are you of their estimate (to the nearest %)? ( in the answer we should find find what value of TINV was used to create this confidence interval, Then plz use trial-and-error to find the value of .)

2-In a random sample of 1,250 household moves, 822 were moves to a location within the same county as the original residence.

1. (a) What is your best estimate of the proportion of all household moves that are to a location within the same county as the original residence.
2. (b) Construct and interpret a 98% confidence interval for that proportion.