Questions: Provide an appropriate response. Use this Standard Normal Table to find the probability between 66.5 and 68.0 inches. If a woman is randomly selected, what is the probability that her height is between 66.5 and 68.0 inches? A. 0.3112 B. 0.1844 C. 0.9608 D. 0.7881

Solution Steps

To find the probability that a woman's height is between 66.5 and 68.0 inches, we first calculate the Z-scores for the given heights using the formula:

\[ Z = \frac{X - \mu}{\sigma} \]

where:

• \(X\) is the height,
• \(\mu = 65\) inches (mean height),
• \(\sigma = 2.5\) inches (standard deviation).

For the lower bound (66.5 inches):

\[ Z_{start} = \frac{66.5 - 65}{2.5} = \frac{1.5}{2.5} = 0.6 \]

For the upper bound (68.0 inches):

\[ Z_{end} = \frac{68.0 - 65}{2.5} = \frac{3.0}{2.5} = 1.2 \]

Next, we find the probabilities corresponding to the calculated Z-scores using the cumulative distribution function \( \Phi(Z) \):

\[ P = \Phi(Z_{end}) - \Phi(Z_{start}) = \Phi(1.2) - \Phi(0.6) \]

From the output, we have:

\[ P = 0.1592 \]

Final Answer