Question

Using the standard normal distribution determine:

a) The area under the curve to the left of z=-2.38

b) The area under the curve to the right of z=1.17

c) The area under the curve between z=-1.52 and z=2.04

Answer 1

For standard normal distribution, we have mean = 0 and standard deviation =1

(A) area under the curve to the left of z=-2.38, means area below z = -2.38

using normalcdf(lower bound, upper bound, mean, stanadard deviation)

setting lower bound = -9999, upper bound = -2.38, mean = 0 and standard deviation = 1

= normalcdf(-9999,-2.38,0,1)

= 0.0087

(B) area under the curve to the right of z=1.17, means area above z = 1.17

using normalcdf(lower bound, upper bound, mean, stanadard deviation)

setting lower bound = 1.17, upper bound = 9999, mean = 0 and standard deviation = 1

= normalcdf(1.17, 9999,0,1)

= 0.1210

(C) area under the curve between z=-1.52 and z=2.04 means area between z=-1.52 and z=2.04

using normalcdf(lower bound, upper bound, mean, stanadard deviation)

setting lower bound = -1.52, upper bound = 2.04, mean = 0 and standard deviation = 1

= normalcdf(-1.52, 2.04,0,1)

= 0.9151