Question

Give the notation and area of these z score

1. above 𝑧 = −2.4

2. below 𝑧 = 0.2

3. Between 𝑧 = −2.3 𝑎𝑛𝑑

𝑧 = −0.98

4. at least 𝑧 = 0.23

5. Between 𝑧 =−1.23 𝑎𝑛𝑑 𝑧 =2

Answer 1

$1. \ P(Z>-2.4) =1-P(Z<-2.4)=\\ =1-0.0082=0.9918;\\ 2. \ P(Z<0.2) =0.5793;\\ 3. \ P(-2.3<Z<-0.98) =\\ =P(Z<-0.98) -P(Z<-2.3)=\\ =0.1635-0.0107=0.1528;\\$

$4. \ P(Z\ge0.23) =1-P(Z<0.23)=\\ =1-0.5910=0.4090;\\ 5. \ P(-1.23<Z<2) =\\ =P(Z<2) -P(Z<-1.23)=\\ =0.9772-0.1093=0.8679\\ \text{(from z-table). }$