Question

Which of the following are true about all normal distributions? Check all that apply A. They...

Which of the following are true about all normal distributions? Check all that apply
A. They are defined by the mean and standard deviation.
B. They are bimodal.
C. They are categorically sharp.
D. They are all centered at zero.


The z-score corresponding to an observed value of a variable tells you the number of standard deviations that the observation is from the mean
A. True
B. False


A positive z-score indicates that the observation is
A. above the mean
B. below the mean

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

Q1. Ans. They are defined by the mean and standard deviation.

Reason : Every normal distribution is categorized by its mean and standard deviation.

They can be unimodal.

Standard normal distribution is always centered at zero not normal distribution.

Q2. Ans. True

Reason : suppose , we say that a variable is 1.5 number of standard deviation from the mean .

I.e x = mean +/- 1.5 sd

x - mean = +/- 1.5 sd

(x- mean)/ sd = +/- 1.5

Here, 1.5 is z score.

Thus, z score is the number of standard deviation an observation is from the mean.

Q3. Ans . Above the mean

Reason: suppose, above formula will result in 1.5 (positive).

It mean that (x - mean)/sd is positive

Thus , (x - mean ) is positive

Which says that x (observation) is above mean .

Please like the answer,Thanks!

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