_I 6. Continuous distributions (a) A uniform distribution has a minimum of -8 and a maximum of 4. Find how much probability mass is between -B and -1. Show calculation. In general, which distribution function answers this kind of question? (b) Between the two curves on the right, 1.00- one represents the distribution of height among American males, and the other represents the heights of American females. Label clearly which curve is which. 0.?5 ' 0 5D - 0.25 ' Which distribution function produces such a curve for the normal distribution? 0.00 ' 5|] 65 7|] F5 EU (c) To join the Illuminati, you have to be richer than 34% of Americans. Assuming incomes are distributed normally, what 2 score would satisfy such a requirement? Show it on the density graph for the standard normal distribution. Label the z score, axes. Show one standard deviation for comparison. (d) In addition to the information in (c), you learn that currently the mean income is $56 and the standard deviation is $15. Use the z score formula to compute the income you should have to be richer than 84% of Americans. Show work