On a test that has a normal distribution, a score of 55 falls two standard deviations above the mean, and a score of 30 falls three standard deviations below the mean. Determine the mean of this test.

Step-by-step explanation:

Given :

Area of Trapezium is 180 cm² .

Height of Trapezium is 15 cm .

One parallel side of trapezium is double of other .

To Find :

Length of two Parallel Sides .

Solution :

\longmapsto\tt{Let\:one\:Parallel\:Side\:be=x}⟼LetoneParallelSidebe=x

As Given that One parallel side of trapezium is double of other . So ,

\longmapsto\tt{Other\:Parallel\:Side=2x}⟼OtherParallelSide=2x

Using Formula :

\longmapsto\tt\boxed{Area\:of\:Trapezium=\dfrac{1}{2}\times{(Sum\:of\:parallel\:sides)}\times{h}}⟼

AreaofTrapezium=

2

1

×(Sumofparallelsides)×h

Putting Values :

\longmapsto\tt{180=\dfrac{1}{2}\times{(x+2x)}\times{15}}⟼180=

2

1

×(x+2x)×15

\longmapsto\tt{180\times{2}=(x+2x)\times{15}}⟼180×2=(x+2x)×15

\longmapsto\tt{360=15x+30x}⟼360=15x+30x

\longmapsto\tt{360=45x}⟼360=45x

\longmapsto\tt{x=\cancel\dfrac{360}{45}}⟼x=

45

360

\longmapsto\tt\bf{x=8}⟼x=8

Value of x is 5 .

Therefore :

\longmapsto\tt{One\:parallel\:side=x}⟼Oneparallelside=x

\longmapsto\tt\bf{8\:cm}⟼8cm

\longmapsto\tt{Other\:parallel\:side=2(8)}⟼Otherparallelside=2(8)

\longmapsto\tt\bf{16\:cm}⟼16cm

So , The Length of Two parallel sides are 8 cm and 16 cm .