Suppose you asked 100 commuters how much they spend each year and obtained a mean of $167 spent on transportation and a standard deviation of $40. Using the 2 SE rule of thumb, calculate a 95% confidence interval for the mean and select the values that come closest to those that would fill the spaces in the following interpretation: we can be 95% confident that the mean amount of money spent on transportation lies between and .

The correct answer is "$159 and $175".

Step-by-step explanation:

The give values are:

Mean,

= $167

Standard deviation,

= $40

Number of commuters,

n = 100

Now,

⇒

On putting the given values, we get

⇒      

⇒      

⇒      

By using the 2 SE rule of thumb, we get

=

=

= ($)

Or,

=

=

= ($)

i.e,

$159 and $175

6 hours 48 min

step-by-step explanation:

68÷5=13.6

13.6×30=408min=6 hours 48 min.

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the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is