What is the probability that the amount of cashew nuts, in a randomly selected packet sold by this company, is between 117.5 grams and 120 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

x = amount of cashew nuts which is N(115,4)

want to find P(117.5 < x < 120)

use transformation z = (x - mean)/SD on above inequality where z is N(0,1):

P(117.5 < x < 120) = P((117.5 - 115)/4) < z < (120 - 115)/4) = P(0.625 < z < 1.25) = P(z < 1.25) - P(z < 0.625) = 0.8944 - 0.7349 = 0.1604.