Juan makes a measurement in a chemistry laboratory and records the result in his lab report. The standard deviation of students' lab measurements is σ = 13 milligrams. Juan repeats the measurement 5 times and records the mean x¯¯¯ of his 5 measurements. (a) What is the standard deviation of Juan's mean result? (That is, if Juan kept on making 5 measurements and averaging them, what would be the standard deviation of all his x¯¯¯′s?) (b) How many times must Juan repeat the measurement to reduce the standard deviation of x¯¯¯ to 2.6?

a) 5.81

b) 25            

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 5

Population standard deviation, σ = 13 milligrams

a) standard deviation of Juan's mean result

5.81 is the standard deviation of Juan's mean result.

b) sample size such that the standard deviation reduces to 2.6

Thus, Juan has to repeat the experiment 25 times to reduce the standard deviation to 2.6

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!