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

a. Normally distributed with mean $30$ and SD $15$

b. skewed to the right with a mean $30$ and SD $15$

c. Normally distributed with mean $0$ and SD $1$

d. skewed to the right with mean $0$ and SD $1$

e. skewed to the right, but the mean and standard deviation cannot be determined without more information.

Short answer

The correct option is (d) skewed to the right with mean $0$ and SD $1$

Step-by-step solution

Given information

With a mean of 30 minutes and a standard deviation of 15 minutes, the distribution of how long it takes different people to complete a crossword puzzle is highly skewed to the right.

Explanation

With a mean of $30$ minutes and a standard deviation of $15$ minutes, the population distribution would be biased to the right. The shape of the $z-$score distribution is always the same as the shape of the population distribution, indicating that the $z-$scores have a right$-$skewed distribution.

However, because $z-$scores are the standardized form of data values, they always have a mean of zero and a standard deviation of one.

Hence, the correct option is (d)