What is the probability that the amount of cashew nuts, in a randomly selected packet sold by this company, is more than 113 grams?

Question

The amount of cashew nuts per packet (𝑌), sold by a company, can be modelled using a normal random variable with a mean of 115.0 grams and a variance of 4.0 grams.

Answer 1

y = grams of nuts

P(Y > 113)

Y is n(115,4)

z = (Y - mean)/SD. where Z is N(0,1)

transform P(Y > 113) using above equation for Z:

P(Y > 113) = P(z > (113-115)/4) = P(z > -0.5) = P(z < 0.5) = 0.6915