The Normal Distribution
A box of cookies contains a mean mass of 180 g with a standard deviation of 2 grams. If the mean mass of these boxes is assumed to be normally distributed, what is the probability a box of cookies will contain less than 179 g? Express your answer to the nearest tenth of one percent.
First we normalize the weight. The the probability of being less than that weight is the probability that a given z score is less than the normalized score.
Given `mu=180,sigma=2,x=179` then `z=(179-180)/2=-.5`
`P(x<179)=P(z<-.5)` . From a standard normal distribution table or technology we find the area under the standard normal curve to the left of z=-.5 (and thus the probability of a given z score to be in this area) to be approximately .3085
The probability that a box weighs less than 179g is approximately 30.9%