Serum glutamic oxaloacetic transaminase (SGOT) is an enzyme thatelevates when the heart muscle is damaged. Assume that thepopulation distribution of SGOT levels in adults with healthyhearts is known to be normally distributed with ? = 18.5 units/Land ? = 13.2 units/L.

a. What proportion of adults with a healthy heart have an SGOTlevel of above 25 units/L? (0.5pts)

b. For a sample size of ? = 40 from this population, what wouldbe the sampling distribution of the mean SGOT level? Include thetype of distribution and the values of the defining parameters.(0.5pts)

c. Now suppose you collected a sample of ? = 40 adults whorecently underwent heart surgery. If the sample mean SGOT level yougot was above 25 units/L, do you think that the SGOT level ofpeople who have recently undergone heart surgery actually has adistribution with ? = 18.5 units/L? Why or why not?

For each of the following scenarios, state the appropriate nullhypothesis and indicate whether the result corresponds to a Type-Ierror, a Type-II error, or no error. Use α=0.05. (1pt each)

a. A new method of relaxation training, which includes mediationand biofeedback, is reported to be successful at reducing highblood pressure, even though it doesn’t actually have any effect onblood pressure.

b. A study that tested if there was any relationship between aperson’s heart rate and consuming a small amount of caffeineresulted in a p-value of 0.21. In truth, there is no relationshipbetween heart rate and caffeine in this population.

c. Park officials tested if new design of bear-proof trash binsis more successful at keeping bears out than the bins theycurrently use. Fact is that the new design is actually moresuccessful than the current one. Their test resulted in a p-valueof 0.08.