Question

The distribution of the time it takes for different people to solve a certain crossword puzzle is strongly skewed to the right, with a mean of 30 minutes and a standard deviation of 15 minutes. the distribution of z-scores for those times is

Answer 1

Answer: Skewed to right with mean 0 and S.D. 1 Explanation: Let's assume the z-scores as a linear transformation. then z=(x-mean)/S.D. = (x-30)/15 z(mean) = (30-30)/15= 0 z(sigma) = 15/15 = 1 Note: Shape does not change.

Answer 2

z-scores illustrates how far a data element is, from the mean of the dataset.

• The distribution of z-scores of the mean is 0
• The distribution of z-scores of the standard deviation is -1

Given

$\mu = 30$ --- the mean

$\sigma = 15$ --- the standard deviation

z-score is calculated using:

$z = \frac{x - \mu}{\sigma}$

(a) The z-score of the mean

This means that:

$x = \mu$

$x = 30$

So, we have:

$z = \frac{x - \mu}{\sigma}$

$z = \frac{30 - 30}{15}$

$z = \frac{0}{15}$

$z = 0$

(b) The z-score of the standard deviation

This means that:

$x = \sigma$

$x = 15$

So, we have:

$z = \frac{x - \mu}{\sigma}$

$z = \frac{15 - 30}{15}$

$z = \frac{-15}{15}$

$z = -1$

Hence, the distributions of z-score for the mean and the standard deviation are 0 and -1 respectively.

Read more about z-scores at:

https://brainly.com/question/13299273