3. An inspector visited a super market and noticed that on the bags of sugar it

Question

3. An inspector visited a super market and noticed that on the bags of sugar it is indicated that the th. The bags were filled by the Sugar Incorporated Company (SIC) which claims that the distribution of the true weight of its bag of sugar is normal wh h mean 2 kg and at random. standard deviation 5 g. The inspector decided to measure the weight of a bag chosen a. What is the probability that the weight is more 2 kg? b. What is the probability that the weight is between 1.99 and 2.01 kg? (Fill in the blank): 5% of the bags have weight less than C. The filling machine used by The Sugar Incorporated Company breaks down from time to time. The Time between breaks (in Weeks) is known to follow a Gamma distribution with shape parameter-6 and rate =0.2. 4. a. What is the probability that the time between breaks exceeds 30 weeks? b. What is the probability the time between breaks is less than 5 weeks? c. What is the average duration of time between breaks? d. Find the 90h percentile of the time between breaks.

Explanation / Answer

3)a) P(X > 2) = P((x - mean)/SD > (2 - 2)/0.005)

= P(Z > 0)

= 1 - (Z < 0)

= 1 - 0.5000 = 0.5

B) P(1.99 < X < 2.01) = P((1.99 - 2)/0.005 < x - mean)/SD < (2.01 - 2)/0.005

= P(-2 < Z < 2)

= P(Z < 2) - P(Z < -2)

= 0.9772 - 0.0228 = 0.9544

C) P(X < x) = 0.05

Or, P(Z < (x - 2)/0.005) = 0.05

Or, (x - 2)/0.005 = -1.645

Or, x = 1.998 = 2

4)a)

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