Final answer:
To find the probability that a randomly selected woman is over 5 feet, 6 inches in height, convert the height into inches. Calculate the z-score using the mean and standard deviation of women's heights. Use a standard normal distribution table to find the probability of a z-score of 1 or greater.
Step-by-step explanation:
To find the probability that a randomly selected woman is over 5 feet, 6 inches in height, we need to convert this height into inches. Since 1 foot is equal to 12 inches, 5 feet is equal to 60 inches. Therefore, 5 feet, 6 inches is equal to 66 inches.
Next, we need to convert this height into standard deviations using the given mean and standard deviation of women's heights. The formula to calculate the z-score is: z = (x - mean) / standard deviation.
Using the formula, we have: z = (66 - 63.6) / 2.5 = 1. Assuming a normal distribution, we can use a standard normal distribution table or a calculator to find the probability of a z-score of 1 or greater.
From the standard normal distribution table or calculator, we find that the probability of a z-score of 1 or greater is approximately 0.1587. Therefore, the probability that a randomly selected woman is over 5 feet, 6 inches in height is approximately 0.1587.