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47.5% of students fall within heights of 100 cm to 120 cm

Step-by-step explanation:

We are given that heights of Grade 1 students are normally distributed

Mean =

Standard deviation =

a)

Empirical rule

68% of data lies within the first standard deviation from the mean i.e

95% of all the data will fall within two standard deviations  i.e.

99.7% of data lies within the three standard deviations i.e.

b)Percentage of students fall within heights of 100 cm to 120 cm

Using the normal distribution curve

Percentage of students fall within heights of 100 cm to 120 cm =

Hence 47.5% of students fall within heights of 100 cm to 120 cm

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.