Questions: Ross enjoys reading scientific books in his free time. Ross reads an average (mean) of 19 books per year with a standard deviation of 4 books depending on his workload. How many books correspond to a standard score of z=3.5 ? -33 books 19 books 29 books 33 books

Solution Steps

We are provided with the following parameters:

• Mean (\( \mu \)): 19 books per year
• Standard Deviation (\( \sigma \)): 4 books
• Z-score (\( z \)): 3.5

The z-score is calculated using the formula:

\[ z = \frac{(X - \mu)}{\sigma} \]

Where:

• \( X \) is the value we want to find (the number of books).

To find \( X \), we rearrange the formula:

\[ X = z \cdot \sigma + \mu \]

Substituting the known values into the rearranged formula:

\[ X = 3.5 \cdot 4 + 19 \]

Now, we perform the calculation:

\[ X = 14 + 19 = 33 \]

Final Answer