# Themean time before failure of the integrated circuits for a

Themean time before failure of the integrated circuits for a simple random sampleof 25 calculators, with a sample mean time of 112 hours, a known standarddeviation of 18 hours, but the distribution is exponential.Ina study to test the effectiveness of nutritional supplements on respiratorytract infections, 337 children were given supplements and 370 were given aplacebo. The days of peak severity in the treatment group had a mean of 6.0days and a standard deviation 2.3 days. The placebo group had a mean of 6.1days and a standard deviation 2.4 days.a) Whatis the 95% confidence interval for the mean number of days for the treatmentgroup?b) Whatis the 95% confidence interval for the mean number of days for the placebogroup?c) Whatdoes the study suggest about the effectiveness of nutritional supplements? 4. MayorFastbuck has 51% of the vote after 1000 randomly-selected ballots have been counted. With a 99% confidence, do you think Fastbuck has stolen wonanother term as mayor?