The standard deviation for the lifetimes of lawn mowers is estimated to be 800 hours (for the entire population). We'd like to collect data and be 97% confident that our margin of error will not exceed 50 hours. What is the minimum sample size we would need to select, to achieve this

So the answer for this case would be n=1206 rounded up to the nearest integer

Step-by-step explanation:

We know the following info:

the standard deviation estimated7

The margin of error is given by this formula:

   (a)

And on this case we have that ME =50 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

  (b)

The critical value for 97% of confidence interval and using a significance level of and , replacing into formula (5) we got:

So the answer for this case would be n=1206 rounded up to the nearest integer

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!

the correct answer would be c