Determine the total area under the standard normal curve in parts (a) through (c

Question

Determine the total area under the standard normal curve in parts (a) through (c) below Click the icon to view a table of areas under the normal curve. (a) Find the area under the normal curve to the left of z=-1 plus the area under the normal curve to the right of z = 1. The combined area is (Round to four decimal places as needed.) (b) Find the area under the normal curve to the left of z-1.57 plus the area under the normal curve to the right of z 257. The combined area is Round to four decimal places as needed,) (c) Find the area under the normal curve to the left of z -0.24 plus the area under the normal curve to the right of z 1.30. The combined area is Round to four decimal places as needed.)

Explanation / Answer

Standard normal curve is symmetrical

P(Z>a) = P(Z<-a)

a)

P(Z<-1) + P(Z>1) = 2*P(Z<-1)= 2*0.1587= 0.3174

b)

P(Z<-1.57) + P(Z>2.57) = P(Z<-1.57) + P(Z<-2.57) = 0.0582 + 0.0051 = 0.0633

c)

P(Z<-0.24) + P(Z>1.30) = P(Z<-0.24) + P(Z<-1.30) = 0.4052 + 0.0968= 0.502

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