A large retirement community has a current population more than 5,000 residents. The distribution of ages of all residents is left skewed with a mean of 65.5 years and a standard deviation of 12.5 year. Suppose you are to conduct a survey and take a random sample of 100 residents of the community. Which of the following corretly describe how to find the probability that you obtain a sample mean age that is younger than 64 years? a) Find the area to the left of z = -0.12 under a standard normal curve. b) Find the area to the right of z = -1.2 under a standard normal curve. c) Find the area to the left of z = -1.2 under a standard normal curve. d) Find the area to the right of z = -0.12 under a standard normal curve. e) None of above

c) Find the area to the left of z = -1.2 under a standard normal curve.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probabiliy distribution

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X, or the area to the left of Z in the normal curve. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X, which is the area to the right of Z in the normal curve.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean and standard deviation , the sample means with size n of at least 30 can be approximated to a normal distribution with mean and standard deviation

In this problem, we have that:

Which of the following corretly describe how to find the probability that you obtain a sample mean age that is younger than 64 years?

Area to the left of z when X = 64 under the standard normal curve. We have to find Z.

Applying the Central Limit Theorem

So the correct answer is:

c) Find the area to the left of z = -1.2 under a standard normal curve.

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 !