Final answer:
The z-score for a woman who is 70 inches tall is calculated to be 1.4. To find how many out of 10,000 women are taller, one would subtract the percentage of women shorter than this height from 100% and then multiply the result by 10,000, using a z-score table.
Step-by-step explanation:
The question involves calculating a z-score for a given height and determining how many individuals out of a larger population would be taller than the given height. To calculate the z-score for a woman who is 70 inches tall:
- First, subtract the mean height (μ = 65 inches) from the individual's height (X = 70 inches).
- Divide the difference by the standard deviation (σ = 3.5 inches).
- The calculation would be z = (X - μ) / σ, which results in z = (70 - 65) / 3.5 = 5 / 3.5 = 1.4.
Thus, the z-score is 1.4 after rounding to the nearest tenth.
To find out how many women out of 10,000 would be taller than the 70 inch tall woman, we would refer to a z-score table (or a standard normal distribution table). However, I will not provide the exact number of women, as I don't have a z-score table included in the question, but I can explain the process.
Using a z-score table, find the percentage of the population with a z-score less than 1.4. Subtract this percentage from 100% to get the percentage who are taller. Multiply this percentage by 10,000 to determine how many women in a sample of 10,000 would be taller than 70 inches.