the common fruit fly is the most studied organism in genetic research because it

Question

the common fruit fly is the most studied organism in genetic research because it is small, is easy to grow, and reproduce rapidly. the length of the thoras (where the wings and legs attach) in a population of male fruit flies is approximately Normal with mean 0.800 milimeters (mm) and standard deviation 0.078 mm

a.) what proportion of flies have thorax lengths less than 0.6mm?

b.) what proportion have thorax length greater than 0.9mm?         

  c.) what proportion have thorax length between 0.6mm and 0.9mm?

Explanation / Answer

We are given,

Mean = 0.8

Standard deviation = 0.078

Z = (x – Mean)/Standard deviation

z = (0.6 – 0.8)/0.078

                 = -2.56

P (z < -2.56)

Now by using Normal Distribution Table we get

P (z<-2.56) = 0.0052

Answer: 0.0052

z = (0.9 – 0.8) /0.078

                 = 1.28

P ( z >1.28 ) = 1 – P ( z < 1.28 )

By using Normal Distribution Table we get,

P ( z <1.28 ) = 0.90

P (z >1.28 ) = 1 – 0.90 = 0.10

Answer: 0.10

z-score for 0.6 = -2.56 (got in part a)

z-score for 0.9 = 1.28 (got in part b)

P (-2.56 < z < 1.28)

= P (z<1.28 ) – P (z<-2.56)

= 0.90 – 0.0052

= 0.8948

Answer: 0.8948

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