Answer: 0.8351
Step-by-step explanation:
Given :Mean : [tex]\mu=\text{ 3 inches}[/tex]
Standard deviation : [tex]\sigma =\text{ 0.5 inch}[/tex]
The formula for z -score :
[tex]z=\dfrac{x-\mu}{\sigma}[/tex]
For x= 2.5 ,
[tex]z=\dfrac{2.5-3}{0.5}=-1[/tex]
For x= 4.25 ,
[tex]z=\dfrac{4.25-3}{0.5}=2.5[/tex]
The p-value = [tex]P(-1<z<2.5)=P(z<2.5)-P(z<-1)[/tex]
[tex]=0.9937903-0.1586553=0.835135\approx0.8351[/tex]
Hence, the probability of picking an apple with diameter between 2.5 and 4.25 inches =0.8351.
