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

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.

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

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

Given

--- the mean

--- the standard deviation

z-score is calculated using:

(a) The z-score of the mean

This means that:

So, we have:

(b) The z-score of the standard deviation

This means that:

So, we have:

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

Read more about z-scores at:

link

Number of adults' tickets (x): $7.50x + $4.00(500 - x) = $3,312.50 $7.50x + $2,000.00 - $4.00x = $3,312.50 $3.50x = $1,312.50 x = 375 
No. of children's tickets (500 - x): = 500 - 375 = 125 
375 adults' tickets, 125 children's tickets 
Proof (Receipts totaled $3,312.50): = (375 tickets * $7.50) + (125 tickets * $4.00) = $2,812.50 + $500.00 = $3,312.50