Statistics

5' Q: A manufacturer knows that their items have a normally distributed lifespan. with a mean of 2 years, and standard deviation of 0.5 years. If 25 items are picked at random, 3% of the time their mean life will be less than how many years? The lengths of pregnancies in a small rural village are normallydistributed with a mean of 270 days and a standard deviation of 14 days. In what range would you expect to nd the middle 95% of most pregnancies? Between :J days and [2 days. If you were to draw samples of size 39 from this population. in what range would you expect to find the middle 95% of most averages for the lengths of pregnancies in the sample? Between D clays and |:] days. The Real Estate Group NY reports that the mean monthly rent for a one-bedroom apartment without a doorman in Manhattan is $2599. Assume the standard deviation is $413. A real estate firm samples 105 apartments. What Is the probability that the sample mean rent Is less than $2,631.24? Engineers must consider the breadths of human heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are normally distributed with a mean of 7.1-in and a standard deviation of 0.9-in. In what range would you expect to nd the middle 95% of most head breadths? lfyou were to draw samples of size 39 from this population, in what range would you expect to find the middle 95% of most averages for the breadths of human heads in the sample? Express the confidence interval 88.4 % :l: 5 % in interval form. :i You measure 37 turtles' weights, and find diey have a mean weight of 57 ounces. Assume the population standard deviation is 10.8 ounces. Based on this, construct a 99% condence interval for the true population mean turtle weight. Give your answers as decimals. to two places :l: ounces You measure 40 dogs' weights, and nd they have a mean weight of 76 ounces. Assume the population standard deviation is 8.7 ounces. Based on this, construct a 90% confidence interval for the true population mean dog weight. Use 2 for the critical value. Give your answers as decimals, to two places :l: ounces