Respuesta :
Answer:
• (a)0.646
,• (b)0.159
,• (c)0.401
,• (d)0.309
,• (e)0.736
Explanation:
• Mean = 20
,• Standard deviation = 8
[tex]Z-\text{Score}=\frac{X-\mu}{\sigma}[/tex]Part A
Area to the left of 23. i,e X=23
First, we find the z-score.
[tex]\begin{gathered} Z=\frac{23-20}{8} \\ =\frac{3}{8} \\ z-\text{score}=0.375 \end{gathered}[/tex]The area to the left of 23 is P(x<23).
From the z-score table:
[tex]\begin{gathered} P\mleft(x<23\mright)=0.64617 \\ P\mleft(x<23\mright)\approx0.646 \end{gathered}[/tex]Part B
Area to the left of 12. i,e X=12
[tex]\begin{gathered} Z=\frac{12-20}{8}=\frac{-8}{8} \\ z-\text{score}=-1 \end{gathered}[/tex]The area to the left of 12 is P(x<12).
From the z-score table:
[tex]P\mleft(x<12\mright)=0.15866\approx0.159[/tex]Part C
Area to the right of 22. i,e X=22
[tex]\begin{gathered} Z=\frac{22-20}{8}=\frac{2}{8} \\ z-\text{score}=0.25 \end{gathered}[/tex]The area to the right of 22 is P(x>22).
From the z-score table:
[tex]P\mleft(x>22\mright)=0.40129\approx0.401[/tex]Part D
Area to the right of 24. i,e X=24
[tex]\begin{gathered} Z=\frac{24-20}{8}=\frac{4}{8} \\ z-\text{score}=0.5 \end{gathered}[/tex]The area to the right of 24 is P(x>24).
From the z-score table:
[tex]P\mleft(x>24\mright)=0.30854\approx0.309[/tex]Part E
The area between 12 and 30
From part B, when X=12, z-Score = -1
When X=30:
[tex]\begin{gathered} Z=\frac{30-20}{8}=\frac{10}{8} \\ z-\text{score}=1.25 \end{gathered}[/tex]Thus, the area between 12 and 30 is:
[tex]P\mleft(-1