Please help me guys
1 answer:
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Answer:
a)
b) Since the sample size is large enough n>30 and the original distribution for the random variable X doesn’t appear to have extreme skewness or outliers, the distribution for the sample mean would be bell shaped and symmetrical.
c)
d) See figure attached
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".
Let X the random variable of interest. We know from the problem that the distribution for the random variable X is given by:
We take a sample of n=40 . That represent the sample size
Part a
From the central limit theorem we know that the distribution for the sample mean is also normal and is given by:
Part b
Since the sample size is large enough n>30 and the original distribution for the random variable X doesn’t appear to have extreme skewness or outliers, the distribution for the sample mean would be bell shaped and symmetrical.
Part c
In order to answer this question we can use the z score in order to find the probabilities, the formula given by:
And we want to find this probability:
We can us the following excel code: "=NORM.DIST(1.807,0,1,TRUE)"
Part d
See the figure attached.
Answer:
(a)
Step-by-step explanation:
(a)The degree of a polynomial is the highest power of the unknown variable in the polynomial.
A polynomial is said to be in standard form when it is arranged in descending order/powers of x.
An example of a fourth degree polynomial is:
We know the polynomial above is in standard form because it is arranged in such a way that the powers of x keeps decreasing.
(b)Polynomials are closed with respect to addition and subtraction. This is as a result of the fact that the powers do not change. Only the coefficients
change. This is illustrated by the two examples below:
The degrees do not change in the above operations. Only the number beside each variable changes. Therefore, the addition and subtraction of polynomials is closed.