Find the proportion of observations (±0.0001) from a standard Normal distribution that falls in each of the following regions. In each case, sketch a standard Normal curve and shade the area representing the region.
(a) z gif. latex?%5Cleqslant ?2.34:
(b) z gif. latex?%5Cgeqslant ?2.34:
(c) z > 1.74:
(d) ?2.34 < z < 1.74:

a) We can use the following excel code to find it:"=NORM.DIST(-2.34,0,1,TRUE)"

b)

c) We can use the following excel code: "=1-NORM.DIST(1.74,0,1,TRUE)"

d) We can use the following excel code: "=NORM.DIST(1.74,0,1,TRUE)-NORM.DIST(-2.34,0,1,TRUE)"

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Part a

We want to find this probability:

And we can use the following excel code to find it:"=NORM.DIST(-2.34,0,1,TRUE)"

Part b

We want to find this probability:

And for this case we can use the complement rule:

And using the result from part a we got:

Part c

We want to find this probability:

And for this case we can use the complement rule:

And we can use the following excel code: "=1-NORM.DIST(1.74,0,1,TRUE)"

Part d

We want to find this probability:

And for this case we can find this probability with this difference:

And we can use the following excel code: "=NORM.DIST(1.74,0,1,TRUE)-NORM.DIST(-2.34,0,1,TRUE)"

b) 1/3 * 1/5

step-by-step explanation:

each smallest part is 1/15 since the written one is 1/5 and it's divided by 3 equal parts. (1/5 )/3 = 1/15 = 1/3 * 1/5