For full credit, you must show All your work and Explain All your answers! Point values given are those I will use If I choose to grade that problem 1. In Project 1 this Fall you studied Recording Times in minutes for Dr. Marion's Sample of 28 Recordings of Mahler's 9th Symphony, which are:

80 82 78 80 89 87 79 90 84 88 81 81 81 86 85 77 84 77 82 85 81 91 82 86 86 89 70 81

h. If µ = 85 and σ = 5, find the probabilities that the:

i. Mean Recording Time of 64 Recordings exceeds 84'30".

ii. Total Recording Time of 100 Recordings exceeds 6 days

I. Using σ = 5, how large a Sample would we need in order to estimate Mean Recording Times for Mahler's 9th Symphony to a:

i. 95% Error Margin of 2 minutes?

ii. 99.5% Error Margin of 48 seconds?

iii. Compare your answers and explain their difference.