A study of 800 homeowners in a certain area showed that the average value of the homes was $82,000 and the standard deviation was $5000. If 50 homes are selected for sale, find the probability that the mean of the values of these homes is more than $83,500. Check to see whether the correction factor should be used. If so, be sure to include it in the computation. Show your work or explain how you obtained your answer. If using the graphing calculator, write the function you are using and the numbers you typed into the calculator. a) Compute the z value first rounded to 2 decimal places. b) Compute the probability that the mean of the values of these homes is more than $83,500.An instructor gives a 100-point examination in which the grades are normally distributed. The mean is 72 and the standard deviation is 8. If there are 5% A's, 5% F's, 20% B's, 20% D's, and 50% C's. Compute the interval of scores in the C, D and F categories. Round the cut off scores to the nearest whole number. Round your z value to two decimal places. NOTE: Show your work or explain clearly how you obtained your answers.A local medical association wants to sponsor a footrace to raise money for cancer research. The average time it takes to run the course is 45 minutes with a standard deviation of 2.8 minutes. If the association decides to award certificates to the fastest 20% of the racers, what should the cutoff time be (round to 1 decimal place)? Show some work or explain how you obtained your answer. When using the calculator write the calculator function you are using including the relevant numerical information or numbers you typed into your calculator