Question

You can insert Desmos graphs or hand-drawn graphs.Draw a normal curve representation for the area, then write thenumerical value of the area under the normal curve for each of thefollowing.A) All values below the meanB) All values to the left of z=-2.17

Answer 1

(a) All values below the mean

The normal curve is a bell shaped curve. The area under the curve between two points tells you the probability of variables taking on a range of values. The total area under the curve is 1 or 100%.

The normal curve representation for the area is:

The area below the mean as shown from the graph include half of the total area. Hence, the area is 50% or 0.5

Hence, the area covered for all values below the mean is 0.5

(b) All values to the left of z= -2.17

The normal curve representation for the area is:

The area to the left of z=-2.17 corresponds the probability P(x < -2.17)

From a normal distribution table, we have:

`P(x\text{ < -2.17\rparen = 0.015003}`

Hence, the area under the curve for values to the ;eft of z=-2.17 is 0.015