6.1 Normal Distribution

Find the area under the standard normal distribution curve between z=0 and z= 1.77

2nd vars -> 2 (normalcdf) -> lower= 0 upper= 1.77 u= 0 o= 1 =0.4616

Properties

1. curve is bell shaped 2. mean, median, and mode are equal and located at the center (also in the middle) 3. uni modal (one mode) 4. curve is symmetrical about the mean 5. curve is continuous. 6. curve never touches x-axis 7. total area under curve= 100% 8. 1 S.D = 0.68 2 S.D = 0.95 3= 0.997

Find the area under the standard normal distribution curve to the left of z = -0.75

lower = -E99 upper = -0.75 u= 0 o= 1 = .2266

Find the z value to the right of the mean so that (a) 54.78% of the area under the distribution curve lies to the left of it. (b) 82.12% of the area under the distribution curve lies to the right of it. (c) 48% of the area under the distribution curve lies between z and -z

(a) invNorm area: .5478 u: 0 o: 1 = 0.12 (b) 1-8212 invNorm(.1788, 0.1) = -.92 (c) 1-.48= 52/2 = .26 100-48=52/2=26+48=74 invNorm(.74,0.1)=.64

Find the area under the standard normal distribution curve to the right of z = 2.01

lower = 2.01 upper = E99 u= 0 o = 1 =.0222

Find the area under the standard normal distribution curve between z=0 and z= -0.32.

normalcdf upper = 0 lower = -0.32 u = 0 o = 1 = -.1255