Given:
The limit problem is:
To find:
The value of the given limit problem.
Solution:
We have,
In the function , the degree of the polynomial is 5, which is an odd number and the leading coefficient is -2, which is a negative number.
So, the function approaches to positive infinity as x approaches to negative infinity.
Therefore, .
Answer:
(a) The distribution of the sample mean () is <em>N</em> (68, 4.74²).
(b) The value of is 0.7642.
(c) The value of is 0.3670.
Step-by-step explanation:
A random sample of size <em>n</em> = 10 is selected from a population.
Let the population be made up of the random variable <em>X</em>.
The mean and standard deviation of <em>X</em> are:
(a)
According to the Central Limit Theorem if we have a population with mean <em>μ</em> and standard deviation <em>σ</em> and we take appropriately huge random samples (<em>n</em> ≥ 30) from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.
Since the sample selected is not large, i.e. <em>n</em> = 10 < 30, for the distribution of the sample mean will be approximately normally distributed, the population from which the sample is selected must be normally distributed.
Then, the mean of the distribution of the sample mean is given by,
And the standard deviation of the distribution of the sample mean is given by,
Thus, the distribution of the sample mean () is <em>N</em> (68, 4.74²).
(b)
Compute the value of as follows:
*Use a <em>z</em>-table for the probability.
Thus, the value of is 0.7642.
(c)
Compute the value of as follows:
Apply continuity correction as follows:
Thus, the value of is 0.3670.