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Question

CSecure httpsowww.webassign.net/weby/student/Assignment Responses/last dep 16189399 -4 points BBBasic Stat7 7.1.008 My Notes My Notes Ask Your Teacher The incubation time for Rhode Island Red chicks is normally distributed with a mean of 24 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.) Area Under a Normal Curve 13.5%: 34% :34% 13.5% )-235% 68% 95% 997% (a) in 20 to 28 days chicks (b) in 22 to 26 days chicks (c) in 24 days or fewer chicks (d) in 18 to 30 days chicks to a Tutor

Explanation / Answer

(a)

20 is 2 standard deviation less from the mean.

28 is 2 standard deviation more than the mean.

Hence the percentage of chicks that would hatch that would lie in 2 standard deviations around the mean would be,

(13.5+34+34+13.5) = 95%.

Hence the number of expected chicks would be 95% of 1000 = 950

(b)

22 is one standard deviation less than mean and 26 is one standard deviation greater than mean. Hence the percentage that lies 1 standard deviation around mean would be (34+34) = 68%.

Therefore the expected number of chicks would be 68% of 1000 = 680

(c)

Since 24 is the mean the percentage of 24 days or fewer would be 50%.

Therefore the expected number of chicks in this case would be 50% of 1000 = 500

(d)

18 is 3 standard deviation less than mean and 30 is 3 standard deviation greater than mean. The percentage that lies around 3 standard deviation from mean would be (2.35+13.5+34+34+13.5+2.35) = 99.7%.

Therefore the expected number of chicks in this case would be 99.7% of 1000 = 997