Suppose that a random man's height from a certain population has a normal distribution with mean of 70" and standard deviation of 3 and a random woman's height has a normal distribution with mean of 66' and standard deviation of 4". find the probability that a random woman is taller than a random man. (hint: the sum of two gaussian random yariables is a gaussian random variable with μ-hs and a variance of σ2-σ2+ ơy2).

(2) (a) you have a simple circuit that consists of only a battery (δvbat=1.5v) and two resistors with resistance r1=10ω and r2=5ω, connected in series with each other. what is the current running through the battery? (b) you re-arrange your circuit so now r2 is attached in parallel to r1 rather than in series. what is the current running through the battery? (c) you add an additional resistor r3=7ω on the same branch as r2. what is the current running through the battery? (d) what is the power dissipated in r3?