Question

In a certain neighborhood, the average number of candies received while trick-or-treating is 50, which a standard deviation of 12. If Isaac received 40 candies, calculate his z-score to the nearest thousandth (3 places after the decimal). (Hint: Use formula x−μσ=z−score
)(1 point)
z=

Answer 1

To calculate the z-score, you can use the formula:

\[
z = \frac{x - \mu}{\sigma}
\]

where:
- \( x \) is the value you want to find the z-score for (in this case, 40 candies received),
- \( \mu \) is the mean (average) number of candies received (50 candies),
- \( \sigma \) is the standard deviation (12 candies).

Substituting in the values:

\[
z = \frac{40 - 50}{12}
\]

Calculating the numerator:

\[
40 - 50 = -10
\]

Now, substituting that into the equation:

\[
z = \frac{-10}{12}
\]

Simplifying:

\[
z = -\frac{10}{12} = -\frac{5}{6} \approx -0.8333
\]

Rounding to the nearest thousandth:

\[
z \approx -0.833
\]

Thus, Isaac's z-score is:

\[
\boxed{-0.833}
\]