Question

The common fruit fly Drosophila melanogaster is the most studied organism in genetic research because it is small, is easy to grow, and reproduces rapidly. The length of the thorax (where the wings and legs attach) in a population of male fruit flies is approximately Normal with mean 0.800 millimeters (mm) and standard deviation 0.078 mm. Use software or Table A. (a) What proportion of flies have thorax length less than 0.55 mm? (Enter your answer as a percentage rounded to two decimal places.) proportion: % (b) What proportion of flies have thorax length greater than 0.87 mm? (Enter your answer as a percentage rounded to two decimal places.) proportion: % (c) What proportion of flies have a thorax of length between 0.55 mm and 0.87 mm? (Enter your answer as a percentage rounded to two decimal places.) proportion:

Answer 1

Solution:

Let X is a random variable shows the length of thorax. Here X has normal distribution with

=0.80,

=0.078

(a)

The z-score for X = 0.55 is

So proportion of flies have thorax lengths less than 0.65 mm is

P(X <0.55 mm) = P(z < -3.205) = 0.0007

(b)

The z-score for X = 0.87 is

So proportion of flies have thorax lengths greater than 0.897 mm is

P(X > 0.87 mm) = P(z > 0.897) =1 - P(z <= 0.897) = 1 - 0.8159 = 0.1841

(c)

The proportion have thorax lengths between 0.55 mm and 0.87 mm is

P(0.55< X < 0.87)= P(-3.205<z<0.897)= P(z < = 0.897) - P(z <= -3.205) = 0.8159 - 0.0007= 0.8152