The common fruit fly Drosophila melanogaster is the most stu

The common fruit fly, Drosophila melanogaster, is the most studied organism in genetic research because it is small, 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 0.8 mm and standard deviation 0.078 mm.

a) What proportion of male fruit flies have thorax length between 0.9 mm and 1 mm

0.0947. 0.0254.     0.5398.

b) About 16% of male fruit flies have thorax length shorter than

0.644 mm. 0.878 mm.     0.722 mm.

Solution

(a) P(0.9<X<1) = P((0.9-0.8)/0.078 <(X-mean)/s <(1-0.8)/0.078)

=P(1.28<Z<2.56) = 0.0947 (from standard normal table)

Answer:0.0947

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(b) P(X<x)=0.16

--> P(Z<(x-0.8)/0.078)=0.16

--> (x-0.8)/0.078 =-0.99 (from standard normal table)

So x= 0.8-0.99*0.078 =0.72278

Answer: 0.722 mm.