We can start by converting 5 ft 10 in to inches:
5 ft 10 in = (5 x 12) + 10 = 70 in
This means that any woman who is at least 70 in tall meets the height requirement for the Beanstalk Club.
To find the percentage of adult women who meet this requirement in the metropolitan area with 500,000 adult women, we need to divide the number of women who meet the requirement by the total number of adult women and then multiply by 100 to express the answer as a percentage.
Let's assume that the distribution of heights among adult women in the metropolitan area is normal, with a mean height of 64 in and a standard deviation of 3 in. We can use the z-score formula to find the percentage of women who are at least 70 in tall:
z = (x - μ) / σ
where x is the height we are interested in (70 in), μ is the mean height (64 in), and σ is the standard deviation (3 in).
z = (70 - 64) / 3 = 2
From a standard normal distribution table, we can find that the percentage of women who are at least 70 in tall is approximately 2.28%.
Therefore, out of the 500,000 adult women in the metropolitan area, we can expect that approximately 2.28% or 11,400 women would meet the height requirement for the Beanstalk Club.