A recent graduate school study of a random sample of 250 US manufacturing companies determined the average financial report preparation time was 68.04 days with a standard deviation of 35.74 days. Calculate to three decimal places the 95 percent confidence interval for the mean report prep time for all US manufacturing companies. [63.001, 72.008] [63.957, 75.568] [63.505, 72.414] [61.612, 74.468] [63.612, 72.468]

And the best option for this case would be

Step-by-step explanation:

Information given

represent the sample mean

population mean

s=35.74 represent the sample standard deviation

n=250 represent the sample size  

Confidence interval

The confidence interval for the mean is given by the following formula:

  (1)

The degrees of freedom are given by:

The Confidence level is 0.95 or 95%, and the significance and , and the critical value for this case woud be

And replacing we got:

And the best option for this case would be

let f (x ) is a function and c be a positive real number,   the graph of the function g (x ) = f (cx ) is represented as follows.

when, c > 1,   the function compresses it in the x - direction.

when, 0 < c < 1, the function stretches it.

the function is g ( x ) = (9x )2.

the heighest power of x in g ( x ) = (9x )2 is 2, so the parent function is square function.

the equation of parent function is f ( x ) = x 2 .

the function is g ( x ) = (9x )2 and the parent function is f ( x ) = x 2 .

so, the functions f and g have the following relationship.

g ( x ) = f ( 9x ).

compare the function g ( x ) = f ( 9x ) with g (x ) = f (cx ).

c = 9 ( > 1 ).

so, the function g (x ) = (9x )2 compresses it in the x - direction.

step-by-step explanation:

8.75

how-to:

first, we need to find what we have to work with.

since i know that we have 7 (years) and 0.8 (inches), we can use these to solve and find the equation!

secondly, what you want to do, is see that we need to know how much growth out of the 0.8 inches he got in only 1 year, instead of 7 years.

let's try to divide.

7 ÷ 0.8 = 8.75