You make cookies to sell that have a mean average of 10 chocolate chips per cookie with a standard deviation of 2 chocolate chips. You bake cookies...
in normally distributed batches of 35. How likely is it to find a randomly chosen cookie that has 7 or less chocolate chips from your last batch of cookies?
Given `mu=10,sigma=2,n=35` :
Find the probability that a randomly selected cookie has fewer than 7 chips.
First we make an adjustment to account for the fact that the number of chips is discrete, while the normal distribution is continuous.
Now convert 6.5 to a z-score:
Then P(x<6.5)=P(z<-1.75) Consulting a standard notrmal table or a calculator we find P(z<-1.75) is approximately 0.0401
The probability of a randomly selected cookie having fewer than 7 chips is approximately 4%.