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)"

Hence, option 'd' is correct.

Step-by-step explanation:

Unlike the expected frequency which is obtained based on prediction, the observed frequency is the actual frequency that is determined from the experiment.

Therefore, we conclude that

Hence, option 'd' is correct.