Answer: 0.0643
Step-by-step explanation:
Given : The diameters of red delicious apples of an orchard have a normal distribution with
Mean : [tex]\mu=3\text{ inches}[/tex]
Standard deviation : [tex]\sigma = 0.5\text{ 0.5 inch}[/tex]
The formula for z -score :
[tex]z=\dfrac{x-\mu}{\sigma}[/tex]
For x= 3.76 inches ,
[tex]z=\dfrac{3.76-3}{0.5}=1.52[/tex]
The p-value = [tex]P(z>1.52)=1-P(z<1.52)[/tex]
[tex]=1-0.9357445=0.0642555\approx0.0643[/tex]
Hence, the probability of picking an apple with diameter greater than 3.76 inches = 0.0643.
