Suppose we will flip a fair coin 100 times. Let X be the number of heads, and use a Normal distribution to approximate the distribution of X.

a. Apply the continuity correction:

P(42<= X<= 58)= P()
(b) Apply the continuity correction:

P(X > =50) = P( X >

(a) P (42 ≤ X ≤ 58) = 0.9108

(b) P (X ≥ 50) = 0.5398

Step-by-step explanation:

The random variable X is defined as the number of heads.

The probability of tossing a Heads in a single flip is, P (X) = p = 0.50.

The coin was flipped n = 100 times.

The random variable thus follows a Binomial distribution with parameters n and p.

As the sample size is too large (n > 30) and the probability of success is closer to 0.50, the binomial distribution can be approximated by the Normal distribution.

The mean of this distribution is: .

The standard deviation of this distribution is:

(a)

Compute the value of P (42 ≤ X ≤ 58) by applying the continuity correction as follows:

After applying the continuity correction the probability statement is:

The probability is:

*Use a z-table for the probability value.

Thus, the value of P (42 ≤ X ≤ 58) by applying the continuity correction is 0.9108.

(b)

Compute the value of P (X ≥ 50) by applying the continuity correction as follows:

After applying the continuity correction the probability statement is:

The probability is:

Thus, the value of P (X ≥ 50) by applying the continuity correction is 0.5398.

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 !

probably .5

i can on others if necessary.