The common fruit fly Drosophila melanogaster is the most studied organism in gen
ID: 3124489 • Letter: T
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 0.770 millimeters (mm) and standard deviation 0.077 mm. (Round your answers to four decimal places.) What proportion of flies have thorax lengths less than 0.67 mm? What proportion have thorax lengths greater than 0.88 mm? What proportion have thorax lengths between 0.67 mm and 0.88 mm?Explanation / Answer
Mean ( u ) =0.77
Standard Deviation ( sd )=0.077
Normal Distribution = Z= X- u / sd ~ N(0,1)
a.
P(X < 0.67) = (0.67-0.77)/0.077
= -0.1/0.077= -1.2987
= P ( Z <-1.2987) From Standard Normal Table
= 0.097
9.7% files have thorax less than 0.67
b.
P(X > 0.88) = (0.88-0.77)/0.077
= 0.11/0.077 = 1.4286
= P ( Z >1.429) From Standard Normal Table
= 0.0766
7.6% files have thorax less than 0.88
c.
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 0.67) = (0.67-0.77)/0.077
= -0.1/0.077 = -1.2987
= P ( Z <-1.2987) From Standard Normal Table
= 0.09702
P(X < 0.88) = (0.88-0.77)/0.077
= 0.11/0.077 = 1.4286
= P ( Z <1.4286) From Standard Normal Table
= 0.92344
P(0.67 < X < 0.88) = 0.92344-0.09702 = 0.8264
82.64% are b/w 0.67 to 0.88 mm