Question

Find the area under the standard normal distribution curve for the following intervals. a. Between z = 0 and z = 2.0 b. To the right of z = 1.5 c. To the left of z = −1.75 d. Between z = −2.78 and z = 1.66

Answer 1

Answer:

a) $P(0$

And we can use the following excel code to find the probability:

"=NORM.DIST(2,0,1,TRUE)-NORM.DIST(0,0,1,TRUE)"

$P(0$

b) $P(Z>1.5) =1-P(Z$

And we can use the following code and we got:

"=1-NORM.DIST(1.5,0,1,TRUE)"

$P(Z>1.5) =1-P(Z$

c) $P(z$

And we can use the following code and we got:

"=NORM.DIST(-1.75,0,1,TRUE)"

$P(z$

d) $P(-2.78$

And we can use the following excel code to find the probability:

"=NORM.DIST(1.66,0,1,TRUE)-NORM.DIST(-2.78,0,1,TRUE)"

$P(-2.78$

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".  

Solution to the problem

Part a

We want this probability:

$P(0$

And we can use the following excel code to find the probability:

"=NORM.DIST(2,0,1,TRUE)-NORM.DIST(0,0,1,TRUE)"

$P(0$

Part b

For this case we want this probability:

$P(Z>1.5)$

And we can use the complement rule and we have:

$P(Z>1.5) =1-P(Z$

And we can use the following code and we got:

"=1-NORM.DIST(1.5,0,1,TRUE)"

$P(Z>1.5) =1-P(Z$

Part c

We want this probability:

$P(z$

And we can use the following code and we got:

"=NORM.DIST(-1.75,0,1,TRUE)"

$P(z$

Part d

We want this probability:

$P(-2.78$

And we can use the following excel code to find the probability:

"=NORM.DIST(1.66,0,1,TRUE)-NORM.DIST(-2.78,0,1,TRUE)"

$P(-2.78$