1. In a normal distribution, determine the proportion of cases that fall in the following ranges (report your answers to four decimal places, as given in Table A in Appendix C of your textbook). For each problem, first sketch the normal curve and shade in the area corresponding to the proportion you are computing.

a.above z = +2.00

b. above z = -1.50

c.below z = -1.82

d. below z = +3.08

e. between z = -1.00 and z = +1.00

f.between z = +.75 and z = +1.25

g.between z = -.75 and z = -1.252.

X

1

3

8

9

1

0

1

1

a. Based on the above data, calculate by hand (using a calculator is ok) the mean and the estimate of the population standard deviation (i.e., use the divisor n - 1). Show work.

b. Transform by hand (using a calculator is ok) the X scores to Z scores. Show work.