Suppose thirty-nine communities have an average of reported cases of larceny per year. Assume that σ is known to be 46.9 cases per year. Find a 90%, 95%, and 98% confidence interval for the population mean annual number of reported larceny cases in such communities. Compare the lengths of the confidence intervals. As the confidence levels increase, do the confidence intervals increase in length?

At wind speeds above 1000 centimeters per second (cm/sec), significant sand-moving events begin to occur. wind speeds below 1000 cm/sec deposit sand and wind speeds above 1000 cm/sec move sand to new locations. the cyclic nature of wind and moving sand determines the shape and location of large dunes. at a test site, the prevailing direction of the wind did not change noticeably. however, the velocity did change. fifty-nine wind speed readings gave an average velocity of x = 1075 cm/sec. based on long-term experience, σ can be assumed to be 245 cm/sec. (a) find a 95% confidence interval for the population mean wind speed at this site. (round your answers to the nearest whole number.) lower limit cm/sec upper limit cm/sec