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".

Part 1

The mean and standard deviation of a normally distributed random variable which has been standardized are one and zero, respectively.

The mean and the deviation for the normal standard distribution are:

$\mu=0, \sigma =1$

So then that's FALSE.

Part 2

Using the standard normal curve, the z−score representing the 10th percentile is 1.28.

We are looking for a value a, that satisfy this:

$P(X>a)=0.90$ (a)

$P(X$ (b)

We can find a z value that satisfy the condition with 0.10 of the area on the left and 0.90 of the area on the right it's z=-1.28. On this case P(Z<-1.28)=0.10 and P(Z>-1.28)=0.90

So that's FALSE.

Part 3

Let z1 be a z−score that is unknown but identifiable by position and area. If the symmetrical area between −z1 and +z1 is 0.9544, the value of z1 is 2.0

If we find this probability:

$P(-2.0< Z$

So on this case we can approximate to 0.9544. And that's TRUE.

Part 4

Using the standard normal curve, the z−score representing the 75th percentile is 0.67.

We are looking for a value a, that satisfy this:

$P(X>a)=0.25$ (a)

$P(X$ (b)

We can find a z value that satisfy the condition with 0.75 of the area on the left and 0.25 of the area on the right it's z=0.67. On this case P(Z<0.67)=0.75 and P(Z>0.67)=0.25

So that's TRUE.

3 0

3 years ago

Which statements are true about these lines? Select three options.

Evgen [1.6K]

Answer:

Line sw has an underfined slope

Line tv has a slope of 0

Line rs and tv are parallel

Step-by-step explanation: I got it right on my quiz

4 0

3 years ago

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