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Many biological measurements on the same species follow a Normal distribution quite closely. The weights of seeds of a variety of winged bean are approximately Normal with mean 525 milligrams (mg) and standard deviation 110 mg.

a) What percent of seeds weigh more than 500 mg?

b) If we discard the lightest 10% of all seeds, what is the smallest weight among the remaining seeds?

c) What percent of seeds weigh between 435mg and 620mg?

d) How much do the heaviest 25% of seeds?

Respuesta :

Answer:

Step-by-step explanation:

Given that many biological measurements on the same species follow a Normal distribution quite closely. The weights of seeds of a variety of winged bean are approximately Normal with mean 525 milligrams (mg) and standard deviation 110 mg.

X = biological measurements on same species

is N(525, 110)

a) P(X>500) = 1-0.4101 = 0.5899

b) Lighest weight are those which are below z = -1.28

Corresponding x score = [tex]525-1.28*110\\= 384.20[/tex]

c) P(435<X<620) = F(620) -F(435)

= 0.8061-0.2066

= 0.5995

In percent = 59.95%

d) Heavies 25% seeds correspond to z = 0.675

X score = [tex]525+0.675*110\\=599.25[/tex]

Above 599.25 mg are the heaviest of the seeds.

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