The average retail price of gasoline for 2014 was 342 cents. What would the standard deviation have to be in order for there to be a 15% probability that a gallon of gas costs less than $3.00?

40.38 cents.

Step-by-step explanation:

In this case, the following formula must be applied:

z = (x-mean) / sd

sd is the standard deviation

If we reorganize, we are left with:

sd = (x-mean) / z

We know that 100 cents is 1 dollar, therefore 342 cents are $ 3.42, that is the value of the average. The value of "x" would be the one we want to compare with, it is $ 3.

z, we must look for it in the normal distribution table, we must look inside the table for the value of 0.15 (15%), which is the closest value, and they would be 0.1492, which corresponds to a value of z of -1.04.

Replacing all the values we are left with:

sd = (3.00-3.42) / - 1.04

sd = 0.4038

Therefore the standard deviation would be $ 0.4038 dollars or 40.38 cents.

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

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