Determine the area under the standard normal curve that lies to the right of (a) Upper Z equals negative 0.77 comma (b) Upper Z equals negative 0.07 comma (c) Upper Z equals negative 0.92 comma and (d) Upper Z equals 0.39 .

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:

[tex] P(Z> -0.77) [/tex]

And using the complement rule and we got:

[tex] P(Z> -0.77) = 1-P(Z<-0.77)[/tex]

And we can use the following excel code:

"=1-NORM.DIST(-0.77,0,1,TRUE)"

And we got:

[tex] P(Z>-0.77) = 0.779[/tex]

Part b

We want this probability:

[tex] P(Z> 0.07) [/tex]

And using the complement rule and we got:

[tex] P(Z> 0.07) = 1-P(Z<0.07)[/tex]

And we can use the following excel code:

"=1-NORM.DIST(0.07,0,1,TRUE)"

And we got:

[tex] P(Z>0.07) = 0.472[/tex]

Part c

We want this probability:

[tex] P(Z> -0.92) [/tex]

And using the complement rule and we got:

[tex] P(Z> -0.92) = 1-P(Z<-0.92)[/tex]

And we can use the following excel code:

"=1-NORM.DIST(-0.92,0,1,TRUE)"

And we got:

[tex] P(Z>-0.92) = 0.821[/tex]

Part d

We want this probability:

[tex] P(Z> 0.39) [/tex]

And using the complement rule and we got:

[tex] P(Z> 0.39) = 1-P(Z<0.39)[/tex]

And we can use the following excel code:

"=1-NORM.DIST(0.39,0,1,TRUE)"

And we got:

[tex] P(Z>0.39) = 0.348[/tex]

Determine the area under the standard normal curve that lies to the right of ​(a) Upper Z equals negative 0.77 comma ​(b) Upper Z equals negative 0.07 comma ​(c) Upper Z equals negative 0.92 comma and ​(d) Upper Z equals 0.39 .

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Determine the area under the standard normal curve that lies to the right of (a) Upper Z equals negative 0.77 comma (b) Upper Z equals negative 0.07 comma (c) Upper Z equals negative 0.92 comma and (d) Upper Z equals 0.39 .