The Normal DistributionA 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...

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.

embizze | High School Teacher | (Level 1) Educator Emeritus

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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%