Question

A company which produces jelly beans claims that the amount, in ounces, of jelly beans in their bags is uniformly distributed on the interval 14 to 18 ounces.

(a) On average, how many ounces of jelly beans are there in a bag? What is the standard deviation?

(b) Assuming that the claim of the company is true, what is the probability that a randomly selected bag contains less than 16.25 ounces?

c) A consumer watch group wants to investigate the claim of the company. They collect a random sample of 40 bags of jelly beans and find that the average number of ounces per bag is 15.6. Assuming that the claim of the company is true, what is the probability that a sample of 40 bags has an average of less than 15.6 ounces of jelly beans per bag. Interpret this result in the context of the problem. What does this indicate about the plausibility of the claim made by the company? You must justify and explain all of your calculations and conclusions.

Answer 1

a)

mean =    (a+b)/2 =    16
      
variance =    (b-a)²/12 =    1.333333333
      
std dev =   √ variance =    1.1547

b)

x=   16.25

P(X ≤ x) =    (x-a)/(b-a) =    0.563

Please revert in case of any doubt.

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