Imagine you have asked 1000 people how much they enjoy eating on a scale of 1-7. You have very skewed data, such that there are only outliers in the "negative" or left-hand side of the distribution. You decide to convert everyone's scores to z-scores. 1. After you convert the scores into z-scores, what would the shape of the distribution be? Explain your answer. Imagine you have ask the same 1000 people how much they enjoy running on a scale of 1-7. You have perfectly normal data. You decide to convert everyone's scores to z-scores. 2. Which z-score would be more probable, a z = -2.0 or a z = +0.5. Explain your answer.

Where the data is distorted and the bad outlier is just axed,when we transform scores of its distribution form into z-score, that become negative or skewed to the left. If n=1000 doesn't have normal skewed knowledge, then:

The data range is between 1 to 7

[tex]\to 1 \ to \ 7 = 6 \sigma \\\\\to \sigma =\frac{7-1}{6} \\\\\to \sigma = \frac{6}{6}\\\\\to \sigma = 1\\\\\mu = 4\\[/tex]

In point (1):

The score that matches:

[tex]\to Z=-2 \ \ \ \mu -26 \\\\ \to 4-2 =2\\\\ \to Z_{score} =2[/tex]

In point (2):

Its value of Z= 0.5 is [tex]\mu \ \ to \ \ 5 \ \ \sigma[/tex]

[tex]= 4+ 0.5 \times 1\\\\= 4+ 0.5\\\\=4.5\\[/tex]