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3 years ago

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From a recent company survey, it is known that the proportion of employees older than 55 and considering retirement is 8%. For a

random sample of size 110, what is standard deviation for the sampling distribution of the sample proportions, rounded to three decimal places?

1 answer:

Akimi4 [234]3 years ago

3 0

Answer: 2.845

Step-by-step explanation:

The formula to find the standard deviation is given by :-

$\sigma=\sqrt{n(1-p)p}$ , where p is the probability of getting success in each trial and n is the sample size.

Given : Sample size : n=110

The proportion of employees older than 55 and considering retirement : p=0.08

Then, the standard deviation is given by :-

$\sigma=\sqrt{110(1-0.08)0.08}\approx2.845347079\approx2.845$

Hence, the standard deviation for the sampling distribution of the sample proportions is 2.845.

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3 years ago

Find the absolute maximum and minimum values of the function below. f(x) = x3 − 9x2 + 3, − 3 2 ≤ x ≤ 12 Solution Since f is cont

Neko [114]

Answer:

There are an absolute minimum (x = 6) and an absolute maximum (x = 12).

Step-by-step explanation:

The correct statement is described below:

Find the absolute maximum and minimum values of the function below:

$f(x) = x^{3}-9\cdot x^{2}+ 3$ , $2 \leq x \leq 12$

Given that function is a polynomial, then we have the guarantee that function is continuous and differentiable and we can use First and Second Derivative Tests.

First, we obtain the first derivative of the function and equalize it to zero:

$f'(x) = 3\cdot x^{2}-18\cdot x$

$3\cdot x^{2}-18\cdot x = 0$

$3\cdot x \cdot (x-6) = 0$ (Eq. 1)

As we can see, only a solution is a valid critical value. That is: $x = 6$

Second, we determine the second derivative formula and evaluate it at the only critical point:

$f''(x) = 6\cdot x -18$ (Eq. 2)

x = 6

$f''(6) = 6\cdot (6)-18$

$f''(6) =18$ (Absolute minimum)

Third, we evaluate the function at each extreme of the given interval and the critical point as well:

x = 2

$f(2) = 2^{3}-9\cdot (2)^{2}+3$

$f(2) = -25$

x = 6

$f(6) = 6^{3}-9\cdot (6)^{2}+3$

$f(6) = -105$

x = 12

$f(12) = 12^{3}-9\cdot (12)^{2}+3$

$f(12) = 435$

There are an absolute minimum (x = 6) and an absolute maximum (x = 12).

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3 years ago

I don't understand this question??

Len [333]

Answer:

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Step-by-step explanation:

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3 years ago

-x + 5y = 14; ( -5, -2 )

Katyanochek1 [597]

-(-5) + 5(-2) = 14

5 -10 = 14

-5 =/= 14

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3 years ago

Rewrite 6(10+2) using the distributive property. Then simply.

Montano1993 [528]

$\begin{gathered} 6(10+2)=(6\cdot10)+(6\cdot2) \\ 6(10+2)=60+12 \\ 6(10+2)=72 \end{gathered}$

Explanation

the distributive property states that multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together

$a(b+c)=ab+ac$

so

Step 1

$6(10+2)$

apply the distributive property

$6(10+2)=(6\cdot10)+(6\cdot2)$

now, calculate ot simplify

$\begin{gathered} 6(10+2)=(6\cdot10)+(6\cdot2) \\ 6(10+2)=60+12 \\ 6(10+2)=72 \end{gathered}$

I hope this helps you

5 0

1 year ago