Question

Suppose a study finds that the wing lengths of houseflies are normally distributed with a mean of 4.55mm and a standard deviation of about 0.392mm. What is the probability that a randomly selected housefly has a wing length between 4mm and 5mm?

Answer 1

Answer: 0.7941

Explanation:

Given : Suppose a study finds that the wing lengths of houseflies are normally distributed with mean : $\mu=4.55\text{ mm}$

$\sigma=0.392\text{ mm}$

Let X be the random variable that represents the wing lengths of a randomly selected housefly.

Z-score : $z=\dfrac{x-\mu}{\sigma}$

For x = 4 mm

$z=\dfrac{4-4.55}{0.392}\approx-1.40$

For x = 5 mm

$z=\dfrac{5-4.55}{0.392}\approx1.15$

Now, the probability that a randomly selected housefly has a wing length between 4mm and 5mm is given by :-

$P(4$

Hence, the probability that a randomly selected housefly has a wing length between 4mm and 5mm is 0.7941 .