In a group of 500 women how many would you expect to be taller than 6 feet?
how!
To determine how many women in a group of 500 would be expected to be taller than 6 feet, we need to have information about the average height and standard deviation of the group. Given that this information is not provided, we can use a general estimate based on population heights.
On average, women tend to be shorter than men, and the distribution of women's heights follows a normal distribution curve. According to data from the National Health and Nutrition Examination Survey (NHANES), the average height for adult women in the United States is around 5 feet 4 inches (162.6 cm), with a standard deviation of approximately 2.7 inches (6.9 cm).
Using this information, we can make an estimation based on the assumption that heights follow a normal distribution. Since the average height is 5 feet 4 inches and the standard deviation is 2.7 inches, we can calculate the proportion of women who would be expected to be taller than 6 feet (72 inches).
To do this, we need to convert the observed height (6 feet) into a z-score, which represents the number of standard deviations an observation is away from the mean. The formula for calculating the z-score is: z = (X - μ) / σ, where X is the observed value, μ is the mean, and σ is the standard deviation.
Calculating the z-score for 6 feet: z = (72 - 64) / 2.7 ≈ 2.96
Next, we can look up the proportion of the population that falls above this z-score in a standard normal distribution table or use a statistical calculator. For a z-score of 2.96, the proportion of the population falling to the right (taller) is approximately 0.0014.
To find the expected number of women taller than 6 feet in a group of 500, we multiply this proportion by the total number of women:
Expected number = 0.0014 * 500 = 0.7
Therefore, based on these estimates, we would expect approximately 0.7 or less than 1 woman out of 500 to be taller than 6 feet.