Question

Using a Nonstandard Normal Distribution. Assume that women's heights are normally distributed with a mean given by µ = 63.6 in. and a standard deviation given by σ = 2.5 in. (based on data from the National Health Survey). Draw a graph, and find the indicated probability or percentage.



Beanstalk Club Height Requirement The Beanstalk Club, a social organization for tall people, has a requirement that women must be at least 70 in. (or 5 ft 10 in.) tall. What percentage of women meet that requirement?

Answer 1

Solution

Women's height $X = N(63.6, 6.25)$, so we are to find the probability $X > 70$, or $(X - 63.6)\frac{1}{2.5} > (70 - 63.6)/2.5 = 2.56$. This is equal to $1 - \Phi(2.56) = 0.01$, where $\Phi$ – distribution function of standard Gaussian random variable.

Answer. $0.01 = 1\%$