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

Question

"The incubation time for Rhode Island Red chicks is normally distributed with a mean of 22 days and standard deviation of approximately 2 days. 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 18 to 26 days

(b) in 20 to 24 days

(c) in 22 days or fewer

(d) in 16 to 28 days

Explanation / Answer

Solution:-
a) in 18 to 26 days
=> z(18) = (18-22)/2
= -4/2 = -2

=> z(26) = (26-22)/2
= 2

Then p(18 < x < 26) = = P(-2 < z < 2) = 0.95
=> 0.95*1000 = 950 eggs

b) in 20 to 24 days

=> z(20) = (20-22)/2
= -2/2 = -1

=> z(24) = (24-22)/2
= 1

Then p(20 < x < 24) = = P(-1 < z < 1) = 0.68

=> 0.68*1000 = 680 eggs

c) in 22 days or fewer
Z(0) = (0-22)/2 = -11
Z(22) = (22-22)/2 = 0
P(0 < x < 22) = P(-11 < z < 0) = 0.50
=> 0.50*1000 = 500 eggs

d) P(16 < x < 28) = 0.9973

=> 0.9973*1000 = 997 eggs

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