Skip to main content
The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1.
Distribusi normal standar adalah distribusi normal dengan rata-rata 0 dan simpangan baku 1.
All normally distributed variables can be transformed into the standard normally distributed variable by using the formula for the standard score:
Semua variabel yang didistribusikan secara normal dapat diubah menjadi variabel yang didistribusikan secara normal standar dengan menggunakan rumus untuk skor standar:

z=value−meanstandarddeviationz = \dfrac{value-mean}{standard deviation}
or
z=X−μσz = \dfrac{X-\mu}{\sigma}

​
Area Under the Standard Normal Curve - Example

​
Question 1

Find the area under the standard normal curve between z = 0 and z=2.34→P(0≤z≤2.34)z = 2.34 \rightarrow P(0 \leq z \leq 2.34).Use your table at the end of the text to find the area.
Standard Normal Distribution

​
Question 2

Find the area under the standard normal curve between z = 0 and z=−1.75→P(−1.75≤z≤0)z = -1.75 \rightarrow P(-1.75 \leq z \leq 0).Use the symmetric property of the normal distribution and your table at the end of the text to find the area.
Standard Normal Distribution

​
Question 3

Find the area to the right of z=1.11→P(z>1.11)z = 1.11 \rightarrow P(z > 1.11).Use your table at the end of the text to find the area.
Standard Normal Distribution

​
Question 4

Find the area to the left of z=−1.93→P(z<−1.93>)z = -1.93 \rightarrow P(z < -1.93>).Use the symmetric property of the normal distribution and your table at the end of the text to find the area.
Standard Normal Distribution

​
Question 5

Find the area between z = 2 and z=2.47→P(2≤z≤2.47)z = 2.47 \rightarrow P(2 \leq z \leq 2.47).Use the symmetric property of the normal distribution and your table at the end of the text to find the area.
Standard Normal Distribution

​
Question 6

Find the area between z = 1.68 and z=−1.37→P(−1.37≤z≤1.68)z = -1.37 \rightarrow P(-1.37 \leq z \leq 1.68).Use the symmetric property of the normal distribution and your table at the end of the text to find the area.
Standard Normal Distribution

​
Question 7

Find the area to the left of z=1.99→P(z<1.99)z = 1.99 \rightarrow P(z < 1.99).Use your table at the end of the text to find the area.
Standard Normal Distribution

​
Question 8

Find the area to the right of z=−1.16→P(z>−1.16)z = -1.16 \rightarrow P(z > -1.16).Use your table at the end of the text to find the area.
Standard Normal Distribution

​
RECALL: The Standard Normal Distribution

z=value−meanstandarddeviationz = \dfrac{value-mean}{standard deviation}
or
z=X−μσz = \dfrac{X-\mu}{\sigma}