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The incubation time for Rhode Island Red chicks is normally distributed with a m

ID: 3350473 • Letter: T

Question

The incubation time for Rhode Island Red chicks is normally distributed with a mean of 25 days and standard deviation of approximately 1 day. Look at the figure below and answer the following questions. If 1000 eggs are being incubated, how many chicks do we expect will hatch in the following time periods? (Note: In this problem, let us agree to think of a single day or a succession of days as a continuous interval of time. Assume all eggs eventually hatch.)

(a) in 23 to 27 days
chicks

(b) in 24 to 26 days
chicks

(c) in 25 days or fewer
chicks

(d) in 22 to 28 days
chicks

Area Under a Normal Curve 2.35% 13.5% 34% 34% 13.5% 2.35% - 3 - 2 - + + 2 + 30 68% 95% 99.7%

Explanation / Answer

SolutionA

normal distr

mean=25

sd=1

P(23<X<27)

z=x-mean/sd

P(23-25/1<Z<27-25/1)

=P(-2<z<2)

=0.9544

np=0.9544*1000=954.4

954 chick

answer :954

Solutionb:

P(24<x<26)

P(24-25/1<Z<26-25/1)

P(-1<Z<1)

=0.6826

np=1000*0.6826=682.6=683 chicks

ANSWER:683

Solutionc:

P(X<25)

P(Z<25-25/1)

P(Z<0)

=0.5

np=1000*0.5=500

ANSWER:500

Solutiond:

P(22<X<28)

P(22-25/1<Z<28-25/1)

P(-3<Z<3)

=0.9987

np=1000*0.9987

=998.7

=999

ANSWER:999