Thread: Normal Distribution PRoblems

(1) The weight W of a person is 100 kg. Unforunately, the weighing machine is not accurate. Suppose the reading R is given by the expression R = W + E where E is the error in the machine and has normal distribution with mean 0 and std. dev. 2.

(a) what is the distribution of the reading given by the weighing machine?

(c) What is the probability that the reading is 2kg more than what the person actually weighs?

Originally Posted by thefirsthokage

(1) The weight W of a person is 100 kg. Unforunately, the weighing machine is not accurate. Suppose the reading R is given by the expression R = W + E where E is the error in the machine and has normal distribution with mean 0 and std. dev. 2.

(a) what is the distribution of the reading given by the weighing machine?

N(W, 4) (normal with mean W and variance 4)

(c) What is the probability that the reading is 2kg more than what the person actually weighs?

2kg is 1 sigma, so we are asking that the probability of z=(R-W)/sigma
(which has a standard normal distribution) be greater that 1. So we look
1 up in the cumulative standard normal distrinution to find

P(z<=1) = 0.8413,

then:

P(z>1) = 1-0.8413 = 0.1587

RonL