Answer: 0.7506
Step-by-step explanation:
Given :Mean : [tex]\mu=\text{ 7.8 grams}[/tex]
Standard deviation : [tex]\sigma =\text{ 0.2 grams}[/tex]
The formula for z -score :
[tex]z=\dfrac{x-\mu}{\sigma}[/tex]
For x= 7.65 ,
[tex]z=\dfrac{7.65-7.8}{0.2}=-0.75[/tex]
For x= 8.2 ,
[tex]z=\dfrac{8.2-7.8}{0.2}=2[/tex]
The p-value = [tex]P(-0.75<z<2)=P(z<2)-P(z<-0.75)[/tex]
[tex]=0.9772498-0.2266274=0.750622\approx0.7506[/tex]
Hence, the probability that the amount of protein is between 7.65 and 8.2 grams=0.7506.
