Answer: 0.7941
Explanation:
Given : Suppose a study finds that the wing lengths of houseflies are normally distributed with mean : [tex]\mu=4.55\text{ mm}[/tex]
[tex]\sigma=0.392\text{ mm}[/tex]
Let X be the random variable that represents the wing lengths of a randomly selected housefly.
Z-score : [tex]z=\dfrac{x-\mu}{\sigma}[/tex]
For x = 4 mm
[tex]z=\dfrac{4-4.55}{0.392}\approx-1.40[/tex]
For x = 5 mm
[tex]z=\dfrac{5-4.55}{0.392}\approx1.15[/tex]
Now, the probability that a randomly selected housefly has a wing length between 4mm and 5mm is given by :-
[tex]P(4<X<5)=P(-1.4<z<1.15)\\\\P(1.15)-P(-1.4)=0.8749281-0.0807567\\\\=0.7941714\approx0.7941[/tex]
Hence, the probability that a randomly selected housefly has a wing length between 4mm and 5mm is 0.7941 .
