Question

The incubation time for a breed of chicks is normally distributed with a mean of 20 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 16 to 24 days chicks

(b) in 18 to 22 days chicks

(c) in 20 days or fewer chicks

(d) in 14 to 26 days chicks

Answer 1

P(X < A) = P(Z < (A - mean)/standard deviation)

a) P(16 < X < 24) = P(X < 24) - P(X < 16)

= P(Z < (24 - 20)/2) - P(Z < (16 - 20)/2)

= P(Z < 2) - P(Z < -2)

= 0.9772 - 0.0228

= 0.9544

0.9544x1000 = 954 chicks

b) P(18 < X < 22) = P(X < 22) - P(X < 18)

= P(Z < (22 - 20)/2) - P(Z < (18 - 20)/2)

= P(Z < 1) - P(Z < -1)

= 0.8413 - 0.1587

= 0.6826

0.6826x1000 = 683 chicks

c) P(X < 20) = 0.5

0.5x1000 = 500 chicks

d) P(14 < X < 26) = P(X < 26) - P(X < 14)

= P(Z < (26 - 20)/2) - P(Z < (14 - 20)/2)

= P(Z < 3) - P(Z < -3)

= 0.9987 - 0.0013

= 0.9974

0.9974x1000 = 997 chicks