the height of 3-year-old boys is approximately normally distributed. Duncan and Shane are 3 year old boys. Duncan is 32.0 inches tall and is in the 32nd percentile. Shane is 34.0 inches tall and is at the 62nd percentile. Which is the closest to the mean

Duncan height is closest to the mean

Step-by-step explanation:

From the question we are told that

  Given that the height of 3-year-old boys is approximately normally distributed then the mean will be the

Hence comparing Duncan height which is in the percentile and Shane height which is in the   percentile with the mean height which is in the

i.e

and

We see that  Duncan height is closest to the mean

1) is right

step-by-step explanation:

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .