Answer:
(a) [tex]P\left ( x\leq 60 \right )=0.9803[/tex], (b) [tex]P\left ( x\geq 50 \right )=0.3156[/tex], (c) [tex]P(50 \leq x \leq 60)=0.2959[/tex]
Step-by-step explanation:
Given that mean [tex]\mu =47[/tex] and standard deviation [tex]\sigma =6.3[/tex]
(a) We need to find [tex]P\left ( x\leq 60 \right )[/tex]. Using z score
[tex]z=\frac{x-\mu }{\sigma }=\frac{60-47}{6.3}=2.063492[/tex]
So,
[tex]P\left ( x\leq 60 \right )=P\left ( z\leq 2.063492 \right )=0.9803[/tex]
(b) We need to find [tex]P\left ( x\geq 50 \right )[/tex]. Using z score
[tex]z=\frac{x-\mu }{\sigma }=\frac{50-47}{6.3}=0.4761904[/tex]
So,
[tex]P\left ( x\geq 50 \right )=P\left ( z\geq 0.4761904 ) \right )=1-P\left ( z\leq 0.4761904 ) \right )=1-0.6844=0.3156[/tex]
(c) We need to find [tex]P(50 \leq x \leq 60)[/tex]. From above z scores
[tex]P(50 \leq x \leq 60)=P\left ( 0.4761904\leq z\leq2.063492 \right )=0.2959[/tex]
