Question

Determine the area under the standard normal curve that lies between

(a) Z= -0.03 and Z=0.03, (b) Z= -1.17 and Z=0, and (c) Z= -1.72 and Z=0.48.

Answer 1

Solution:-

a) The area under the standard normal curve that lies between Z = - 0.03 and Z = 0.03 is 0.024.

z₁ = - 0.03

z₂ = 0.03

P( -0.03 < z < 0.03) = P(z > - 0.03) - P(z > 0.03)

P( -0.03 < z < 0.03) = 0.512 - 0.488

P( -0.03 < z < 0.03) = 0.024

b) The area under the standard normal curve that lies between Z = - 1.17 and Z = 0.0 is 0.379 .

z₁ = - 1.17

z₂ = 0.0

P( -1.17 < z < 0) = P(z > - 1.17) - P(z > 0)

P( -1.17 < z < 0) = 0.879 - 0.50

P( -1.17 < z < 0) = 0.379

c) The area under the standard normal curve that lies between Z = - 1.72 and Z = 0.48 is 0.6417.

z₁ = - 1.72

z₂ = 0.48

P( -1.72 < z < 0.48) = P(z > - 1.72) - P(z > 0.48)

P( -1.72 < z < 0.48) = 0.9573 - 0.3156

P( -1.72 < z < 0.48) = 0.6417