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Probability / Statistics: Problem #3

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Salt is packed in bags labelled 1kg. The weight of the bags is found to be normally distributed. The probability that a bag weighs less than 995 grams is 0.0214 and the probability that a bag weighs more than 1005 grams is 0.1450.

(a) Calculate the mean weight and standard deviation of the salt bags. Give your answers in grams correct to 2 decimal places.

(b) What is the probability that a bag will weigh at least 1kg?

(c) If bags that weigh less than 1kg are discarded, what percentage (to 2 decimal places) of bags will be discarded (i.e. thrown away)?

Bags weighing at least 1kg are put in boxes

(d) What is the probability that a bag being put in a box will weigh more than 1005 grams?

Each box contains 20 bags. A box is chosen at random

(e) What is the probability that no more than 5 bags in the box weigh more than 1005 grams?

(f) What is the expected number of bags in the box that will weigh more 1005 grams?

(g) If ten boxes are selected, what is the probability there will be less than six boxes with no more than 5 bags weighing more than 1005 grams?
 
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