The mean height of women in the United States is 63.5 inches with a standard deviation of 2.5 inches. Determine the probability that a woman selected at random is taller than 67 inches.
To determine this probability, we need to use the z-score formula:
z = (X - μ) / σ
where:
- X is the value we are interested in (67 inches)
- μ is the mean height of women in the United States (63.5 inches)
- σ is the standard deviation (2.5 inches)
First, we calculate the z-score:
z = (67 - 63.5) / 2.5
z = 1.4
Next, we look up the z-score in a standard normal distribution table (or use a calculator) to find the corresponding probability.
From the standard normal distribution table, we find that the probability of a z-score being less than 1.4 is approximately 0.9192. Therefore, the probability of a woman selected at random being taller than 67 inches is 1 - 0.9192 = 0.0808, or 8.08%.