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wolverine [178]
3 years ago
9

Consider a large population with a mean of 150 and standard deviation of 27. a random sample of size 25 is taken from the popula

tion. calculate the standard error of the sampling distribution of this sample mean and round your answer to the hundredths place.
Mathematics
1 answer:
Karolina [17]3 years ago
5 0

Answer:

Standard error = 5.4

Step-by-step explanation:

We are given that Population Mean, \mu = 150 and Population Standard deviation, \sigma = 27  and sample size, n = 25

Standard error formula for the sampling distribution of this sample mean is given by;

<em>  Standard error</em> = \frac{\sigma}{\sqrt{n} } = \frac{27}{\sqrt{25} } = 5.4

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Answer:

1.  \( f\circ g(x)=0.05x-150

2. \( g\circ f(x)=0.05x-3000

3. The first one represents Dale's commission

Explanation:

1. The composition of the function

                                                             \( f\circ g(x)=f(g(x)) \)    

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That is:

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  • g(x) = x - 3000

       f(g(x)=0.05(x - 3000)

       f(g(x))=0.05x-150

2. The composition of the function

                                                             \( g\circ f(x)=g(f(x)) \)                                                                  

means that you first apply the function f(x) and then g(x) on the output of f(x).

That is:

      g(f(x))=((0.05x)-3000)=0.05x-3000

3. Which one represents Dale's commission

To calculate Dales's commision you must subtract $3,000 from the sales, to find the sales over $3000. That is: x - 3,000, which is the function g(x).

Therefore, you first use g(x).

Then, you must multiply the output of g(x) by 0.05 to find the 5% of the sales over $3,000. That is: 0.05(g((x)) = 0.05(x - 3000) = 0.05x - 150.

Therefore, the composition that represents Dale's commission is the first one:

  f(g(x)=0.05(x - 3000)

       f(g(x))=0.05x-150

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