Question

adult men have heights with a mean of 69.0 inches and a standard deviation of 2.8 inches. find the height of a man with a z - score of 3.8929 (to 4 decimal places)

Explanation:

Step1: Recall z-score formula

\( z = \frac{x - \mu}{\sigma} \)

Step2: Rearrange to solve for x

\( x = \mu + z\sigma \)

Step3: Substitute values

\( x = 69.0 + 3.8929 \times 2.8 \)

Step4: Calculate product

\( 3.8929 \times 2.8 = 10.89912 \)

Step5: Add to mean

\( x = 69.0 + 10.89912 = 79.89912 \)

Step6: Round to 4 decimals

\( x \approx 79.8991 \)

Answer:

79.8991