Have you ever tried to get out of jury duty? About 25% of those called will find an excuse (work, poor health, travel out of town, etc.) to avoid jury duty†. If 15 people are called for jury duty, find the following. a) What is the probability that all 15 will be available to serve on the jury? (Round your answer to three decimal places.)(b) What is the probability that 9 or more will not be available to serve on the jury? (Round your answer to three decimal places.)(c) Find the expected number of those available to serve on the jury. What is the standard deviation? (Round your answers to two decimal places.)μ =σ =(d) How many people n must the jury commissioner contact to be 95.9% sure of finding at least 12 people who are available to serve? (Enter your answer as a whole number.)

Step-by-step explanation:

a) About 25% of those called will find an excuse (work, poor health, travel out of town, etc. to avoid jury duty. So, the probability that a jury will be available to serve is ; P = 1 - q = 1 - 0.25 = 0.75

Given n = 15 and  p = 0.75

P(X = 15) = Binompdf(15, 0.75, 15) = 0.013

b) Event "9 or more will not be available to serve on the jury" is equivalent to "6 or less will be available to serve".

P(X ≤ 6) = Binompdf(15, 0.75, 6) = 0.004

c) The expected number and the standard deviation of those available to serve on the jury are: μ = np = 15(0.75) = 11.25

σ = √np(1 - p) = √15(0.75)(1 - 0.75) = 1.68

d) Use function:

P(X ≥ 12) = 1 - P(X ≤ 11) = 1 - Binompdf(n, 0.75, 11)

By using above function, the probabilities of P(X ≥ 12) at different sample size are shown below:

nP(X ≥ 12)

120.032

130.127

140.281

150.461

160.630

170.765

180.861

190.923

200.959

210.979

Therefore, The jury commissioner must contact at least 20 people to be 95.9% sure of finding at least 12 people who are available to serve.

the population of other specie of birds will decline or other specie of birds will find some alternate source of food to survive.

explanation:

according to the competitive exclusion principle, which is also known as gause's law, two specie living in the same niche and feeding on the same resource cannot co-exist stably.

as we have well studied the theory of natural selection which states that only those organisms survive which have better tendency to compete for food and adapt to the environmental conditions.

coming towards the question, what wi ll happen when one species outcompetes the other for the small fish , the other specie will not get enough food and will start to die or decline in population. eventually either other specie needs to find another alternative food source for itself or migrate at some other location where there is less competition otherwise it will just not exist anymore at that niche.

hope it !