a) Which of the following properties distinguishes the standard normal distribution from

Reeves

Reeves

Answered question

2021-01-13

a) Which of the following properties distinguishes the standard normal distribution from other normal distributions?
-The mean is located at the center of the distribution.
-The total area under the curve is equal to 1.00.
-The curve is continuous.
-The mean is 0 and the standard deviation is 1.
b) Find the probability P(z<0.51) using the standard normal distribution.
c) Find the probability P(z>0.59) using the standard normal distribution.

Answer & Explanation

Tuthornt

Tuthornt

Skilled2021-01-14Added 107 answers

Step 1
Standard Normal Distribution is symmetric continuous distribution with mean 0 and variance 1.
-The mean is located at the center of the distribution.
This is True because here the center of the distribution is 0 and the mean is also 0.
-The total area under the curve is equal to 1.00.
This is True because area under curve of any distribution will be always 1
-The curve is continuous.
This is True because it takes values on continuous domain
-The mean is 0 and the standard deviation is 1.
This is True by the definition of Standard Normal Distribution.
Step 2
b. P(Z<0.51)=Φ(0.51)=0.305026[From the table of Standard Normal Distribution,Φ is the CDF of Standard Normal Distribution]
c. P(z>0.59)=1Φ(0.59)=10.277595=0.722405[From the table of Standard Normal Distribution,Φ is the CDF of Standard Normal Distribution]

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