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nadezda [96]
2 years ago
15

A study of the career paths of hotel general managers sent questionnaires to an SRS of 210 hotels belonging to major U.S. hotel

chains. There were 108 responses. The average time these 108 general managers had spent with their current company was 8.8 years. (Take it as known that the standard deviation of time with the company for all general managers is 3.5 years.)
Required:
a. Find the margin of error for an 85% confidence interval to estimate the mean time a general manager had spent with their current company.
b. Find the margin of error for a 99% confidence interval to estimate the mean time a general manager had spent with their current company.
Mathematics
1 answer:
Tema [17]2 years ago
7 0

Answer:

a

  E = 0.4850  

b

 E = 0.8689  

Step-by-step explanation:

From the question we are told that

   The sample size is  n  =  108

    The sample mean is  \= x  =  8.8 \ years  

     The standard deviation is  \sigma = 3.5

From the question we are told the confidence level is  85% , hence the level of significance is    

      \alpha = (100 - 85 ) \%

=>   \alpha = 0.15

Generally from the normal distribution table the critical value  of  \frac{\alpha }{2} is  

   Z_{\frac{\alpha }{2} } = 1.44

Generally the margin of error is mathematically represented as  

      E = Z_{\frac{\alpha }{2} } *  \frac{\sigma }{\sqrt{n} }

=>    E = 1.44 *  \frac{ 3.5 }{\sqrt{108} }

=>    E = 0.4850  

From the question we are told the confidence level is  99% , hence the level of significance is    

      \alpha = (100 - 99 ) \%

=>   \alpha = 0.01

Generally from the normal distribution table the critical value  of  \frac{\alpha }{2} is  

   Z_{\frac{\alpha }{2} } = 2.58

Generally the margin of error is mathematically represented as  

      E = Z_{\frac{\alpha }{2} } *  \frac{\sigma }{\sqrt{n} }

=>    E = 2.58 *  \frac{ 3.5 }{\sqrt{108} }

=>    E = 0.8689  

 

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Step-by-step explanation:

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Si la época prehistórica sucedió desde hace 2.5 millones de años a.C., hasta hace 2.500 años a.C.; el período Paleolítico (2.5 m
tia_tia [17]

Answer:

El período paleolítico corresponde a \frac{332}{333} de la época prehistórica.

Step-by-step explanation:

En primer lugar, se determina la extensión de tiempo, medida en años, tanto de la época prehistórica como el período paleolítico: (Nótese que el signo negativo significa a.C.)

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\Delta t = -10000 - (-2500000)

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La fracción de la época prehistórica que corresponde al período paleolítico es:

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3 years ago
6 * ( 12 - 7.5 ) - 7
Paladinen [302]

Answer: 20

Explanation: Alright, so basically you’re going to want to use PEMDAS (Parenthesis, Exponents, Multiplication/ Division, Addition/ Subtraction)

* just means multiply.. sooo the problem looks like this:

6x(12-7.5)-7

We’ll start at the parentheses :)

So (12-7.5) = 4.5

Now our problem looks like: 6x(4.5)-7

Following PEMDAS, the next thing to come up is multiplication! So we’re going to multiply 6 by 4.5 ...

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After this our problem looks like: 27-7

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5 0
3 years ago
Read 2 more answers
For which value(s) of x are the triangles congruent?​
Varvara68 [4.7K]

Step-by-step explanation:

The solutions are 2 and 5

Because it's asking what would make the triangles congruent, you would set up the equation like this because the angles (angle 3 and angle 4) need to be equal:

x^2 = 7x - 10

Next, you add 10 to both sides. This is so that you can move it to the other side, addition is the inverse of subtraction.

x^2 + 10 = 7x

Now subtract 7x from both sides. Subtraction is the inverse of addition. You do this to get it on the other side so you can factor it. You can move the 10 and 7x to the other side in any order or at the same time, I just did it like this.

x^2 - 7x + 10 = 0

Now, factor. I don't really know how to explain factoring, you just get a feel for it with a lot of practice.

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You can use FOIL to check this if you want to. x(x) is x^2, -2(-5) is 10), -2x - -5x is -7x. Now, find what you need to do to make what's in each of the groups of parentheses equal to 0.

x - 2 = 0

x = 2

One of the solutions is 2, because you add 2 to x to get 0.

x - 5 = 0

x = 5

The other solution is 5, because you add 5 to x to get 0. Lastly, check your solutions by plugging them in to the original equation.

2^2 = 7(2) - 10

4 = 14 - 10

So 2 is definitely a solution.

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25 = 35 - 10

5 is also a solution.

Hope that helps :]

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