A random sample of 110 lightning flashes in a certain region resulted in a sample average radar echo duration of 0.81 second and a sample standard deviation of 0.34 second. (a) Calculate a 99% confidence interval for the true average echo duration. (b) This sample data is used as a pilot study, and now the investigator would like to design a new study to construct a 99% confidence interval with width 0.1. What is the necessary sample size?

Suppose babies born after a gestation period of 32 to 35 weeks have a mean weight of 25002500 grams and a standard deviation of 800800 grams while babies born after a gestation period of 40 weeks have a mean weight of 27002700 grams and a standard deviation of 385385 grams. if a 3232-week gestation period baby weighs 21252125 grams and a 4040-week gestation period baby weighs 23252325 grams, find the corresponding z-scores. which baby weighs lessless relative to the gestation period?