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
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
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