1) The average length of actual running time (excluding advertisements) for television feature films is 1 hour and 40 minutes, with a standard deviation of 15 minutes. If a sample of 49 television feature films is taken at random, what is the probability that the average running time for this group is 1 hour and 45 minutes or more?
2) A quality control engineer is concerned about the breaking strength of a metal wire manufactured to stringent specifications. A sample of size 25 is randomly obtained, and the breaking strengths are recorded. The breaking strength of the wire is considered to be normally distributed with a standard deviation of 3. Find a 95% confidence interval for the mean breaking strength of the wire.
26, 27, 18, 23, 24, 20, 21, 24, 19, 27, 25, 20, 24, 21, 26, 19, 21, 20, 25, 20, 23, 25, 21, 20, 21.
3) An investment advisor believes that the return on interest-sensitive stocks is approximately normally distributed. A sample of 24 interest-sensitive stocks was selected, and their yearly return (including dividends and capital appreciation) was as follows (in percentages):
11.1, 12.5, 13.6, 9.1, 8.7, 10.6, 12.5, 15.6, 13.8, 8.0, 10.9, 7.6
5.2, 1.2, 12.8, 16.7, 13.9, 10.1, 9.6, 10.8, 11.6, 12.3, 12.9, 11.6
Find a 90% confidence interval for the mean yearly return on the interest-sensitive stocks.
4) If a sample size of 70 was necessary to estimate the mean of a normal population to within 1.2 with 90% confidence, what is the approximate value of the standard deviation of the population?