Question

The incubation time for Rhode Island Red chicks is normally distributed with a mean of 23 days and standard deviation of approximately 3 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 17 to 29 days ____chicks

(b) in 20 to 26 days ____chicks

(c) in 23 days or fewer ____chicks

(d) in 14 to 32 days_____ chicks

Answer 1

We use the empirical rule of normal distribution here.

a) 17 = 23 - 2*3 that is 2 standard deviations less than the mean. Also, 29 = 23 + 2*3 that is 2 standard deviations more than the mean. According to the empirical rule, 95% of the observations lies within two standard deviations from the mean. Therefore expected number of eggs hatching in 17 to 29 days is given as 95% of the eggs that is 950 eggs.

b) According to the empirical rule, 68% of the observations lies within one standard deviation from the mean. Therefore expected number of eggs hatching in 20 to 26 days is given as 68% of the eggs that is 680 eggs

c) As 23 is the mean of the distribution and the normal distribution is symmetric about the mean. Therefore about 500 eggs are expected to be hatched in 23 days or lower.

d) 14 is 3 standard deviations less than mean and 32 is 3 standard deviations more than mean. According to empirical rule, 99.7% of the observations lies within 3 standard deviations from the mean. Therefore 997 eggs are expected to hatch in that time period.