The incubation time for a breed of chicks is normally distributed with a mean of
ID: 2948759 • Letter: T
Question
The incubation time for a breed of chicks is normally distributed with a mean of 30 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 or a succession of days 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 as a continuous interval of time. Assume all eggs eventually hatch.) Area Uader a Normal Cure 13.5% 34% MK 13.5 : 35% 95% 997% (a) in 24 to 36 days chicks (b) in 27 to 33 days chicks (c) in 30 days or fewer chicks (d) in 21 to 39 days chicks
Explanation / Answer
Soln,
Given data that
Incubated chicks as 1000 hence n =1000
Also given the distribution gor 30 days which is normally distributed as the graph is bell shape
Also standard deviation is 3 days
So
a. In 24 to 30 days as the mean days are 30 days so the are under the 24 and 30 days is 2 standard deviations
Hence from the graph it is evident that under this area 95 % of data lies qq11QQqqQ1q11Aa1qq1qqqqqhence (1000*95)/100 =950 , hence in 24 to 36 days 950 chicks are being incubated incubated.
b) similarly for 27 to 30 days it lies between .1 standard deviation hence from graph it is evident that 68 % of data lies under 27 to 30 days this means (1000*68)/100= 680 chicks are being incubated.
c) here also in 30 days or fewer 50 % of the data lies as in graph hence (1000*50)/100=500 chicks are being incubated.
d) Here again within 21 to 39 days the data is under 3 standard deviation , and as from graph above it is evident that 99.7 % of data lies under this time period hence (1000*99.7)/100=997 no chicks are being incubated under this period.
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