# Find the value where two normal distributions have equal probability.

Having difficulty with these questions from my one of my modules

In a certain population women have weights which are Normally distributed with a mean of 50kg and a standard deviation of 5kg. Men have weights which are Normally distributed with a mean of 70kg and a standard deviation of 10kg.

A) Find a weight w to the nearest 0.1kg such that both men and women would have an equal probability of having a weight between w and w+1 kg.

B) How many points of equal probability are there?

• Is the proportion of men and woman 50/50? May 1 '18 at 16:21
• To start, represent $w = 70+10k_1$ and $w+1 = 70+10k_2$. This allows you to solve for $k_1,k_2$. You want the difference in probabilities for these $z$-scores to be equal to the difference in probabilities between $z$-scores of $l_1,l_2$ where $w=50+5l_1$ and $w+1=50+5l_2$. Something to that effect. May 1 '18 at 16:22
• wolframalpha.com/input/… Wolframalpha finds two solutions. May 1 '18 at 16:29