Suppose a tire manufacturer states the average lifetime of t…

Suppose a tire manufacturer states the average lifetime of their tires is 70,000 miles, with a standard deviation of 1,500 miles. Consider a random sample of 38 tires from this manufacturer. (Round to 3 decimal places.)   a. Find the standard deviation of the sample mean.  b. Find the probability that the sample mean is greater than 69,500 miles.

A local news station is interested in the proportion of loca…

A local news station is interested in the proportion of local residents that regularly get their news source from them rather than on the internet. A researcher randomly selects 140 residents, and found that 58 use the local news station for their news source. (Round to 3 decimal places.)   a. Calculate a 95% confidence interval for the proportion of all local residents that use the local news station for their news source (input your interval as “(a, b)”, where a is the lower limit and b is the upper limit of the interval)  b. Interpret the interval from part a (write out a sentence and be specific): We are 95% confident that c. How many local residents need to be sampled in order to estimate the proportion to within 4% with 95% confidence?