Question

Some study on human pregnancies were conducted and it is found that, human pregnancies have a gestation period that is approximately normal with $\mu = 39$ weeks and $\sigma = 2$ weeks. What is the z-score for a pregnancy that lasts 36 weeks?

• A. -1.5
• B. +1.5
• C. -1.14
• D. +1.14

Hint:

Use $z = \dfrac{X - \mu}{\sigma}$ to standardize any normal distribution problem.

Answer 1

The Correct Option is A

Step 1: Recall z-score formula.
\[ z = \frac{X - \mu}{\sigma} \] where $X$ = observed value, $\mu$ = mean, $\sigma$ = standard deviation.
Step 2: Substitute given values.
Here, $X = 36$, $\mu = 39$, $\sigma = 2$.
\[ z = \frac{36 - 39}{2} = \frac{-3}{2} = -1.5 \] Step 3: Interpretation.
A z-score of -1.5 means that a pregnancy lasting 36 weeks is 1.5 standard deviations below the mean gestation length.
Step 4: Conclusion.
Therefore, the z-score is -1.5.