z-scores also follow a normal distribution with: µ=0 & σ=1 True or false?

z-scores also follow a normal distribution with: µ=0 & σ=1

True or false?

Solutions

Expert Solution

solution:

Yes, True : z-scores also follows a normal distribution with mean () = 0 and standard deviation () = 1

Reasoning:

Normal distribution: It is a probability distribution that is symmetric about mean, and showing the data near the mean are the most frequent in occurrence than the data far from the mean.It is also known as "Gaussian Distribution".The graph of the normal distribution will appear as 'bell curve'.

Properties of normal distribution:

-----> The distribution of curve is "Bell shaped"

-----> The curve is symmetric about mean. In normal distribution mean = mode = median

-----> The area under the curve is 1

standard normal distribution: Standard normal distribution is a special type of normal distribution.It is the distribution that occurs when the normal distribution has mean = 0 and standard deviation = 1.It has the same properties as the normal distribution.

Let X be the normal random variable and Z (z-scores) be the standard normal variable then the relation between

X and Z is

X = + Z()

For standard normal distribution,we know that

mean () = 0 and standard deviation () = 1

Then X = Z

which implies Z also follows normal distribution mean () = 0 and standard deviation () = 1.

Answer: True

orchestra answered 1 year ago

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