SOLUTION: 4. A manufacturer fills jars with coffee. The weight of coffee, W grams, in a jar can be modelled by a normal distribution with mean 232 grams and standard deviation 5 grams. (i)

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Question 1150536: 4. A manufacturer fills jars with coffee. The weight of coffee, W grams, in a jar can be modelled by a normal distribution with mean 232 grams and standard deviation 5 grams.
(i) Find P(W < 227)? [4 marks]
(ii) One hundred jars of coffee are selected at random. Find the probability that more than 23 jars contains less than 227 grams of coffee.
Answer by Glaviolette(140) (Show Source):
You can put this solution on YOUR website!
(i) z = (227-232)/5 = -1
P(W < 227) = .1587 (from z-score table)
(ii) To determine the probability that more than 23 jars out of 100 weigh less than 227 grams, I would use a binomial distribution. More than 23 weighing less than 227 is the same as 76 or less weighing more than 227.
P(> 23 of 100 weigh less than 227) = P(< or = 76 weighing more than 227)
= binomcdf(100, .8413, 76)
= .0225
OR More than 23 weighing less than 227 is the complement of 23 or less weighing less than 227
P(> 23 of 100 weigh less than 227) = 1 - P(< or = 23 less than 227)
= 1 - .9774
= .0225