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The incubation time for a breed of chicks is normally distributed with a mean of 20 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 18 to 22 days

chicks

(b) in 19 to 21 days

chicks

(c) in 20 days or fewer

chicks

(d) in 17 to 23 days

chicks

Guest Dec 13, 2018

#2**+1 **

\(\text{Let }\Phi(x) \text{ be the CDF of the standard normal distribution}\\ P[n \leq N] = \Phi\left(\dfrac{N-\mu}{\sigma}\right)\\ P[N < n] = 1-P[n \leq N] \\ P[N_l \leq n \leq N_h] = \Phi\left(\dfrac{N_h-\mu}{\sigma}\right) - \Phi\left(\dfrac{N_l-\mu}{\sigma}\right)\)

now just dump your numbers in

Rom Dec 13, 2018