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Any help much appreciated!
Q1. In the mass production of jars of Goldtaste coffee, the probability that a jar of coffee is rejected because it is underweight is 5%. If random samples of 10 jars are selected for inspection, find the probability that in any such sample:
i) three jars are rejected.
ii) At most three jars are rejected.
If two random samples of 10 jars are selected at the same time:
iii) Find the probability that no jars are rejected in either sample.
iv) find the probability that one jar is rejected
Suppose that p = Probability that out of a random sample of n jars, there is at least 1 acceptable jar. If P > 0.09999992, show that 0.0000008 > (0.05)^n and hence find the min value of n.
Q2: A machine produces components in batches of 20000. At the beginning of production, the machine is set to produce the required mean length of components at 30mm and then be set to give any of 3 standard deviations:
Setting 1 0.12 mm - cost of this setting S.D. = £850
Setting 2 0.15 mm - cost of setting this standard deviation = £550
Setting 3 0.18 mm - Cost of setting this S.D. = £100
Any length produced must lie between 29.65mm and 30.41 mm, otherwise it is classed as defective and costs the company £1. You can assume the length of a component is Normally distributed. Which S.D. should be used if the decision is to be purely based on combined cost of setting the machine and of the defectives?
cheers
Completely confused. Any help much appreciated!
Q1: The daily receipts of a fast food franchise outlet are normally distributed with mean £5000 and S.D. £500.
a) what is the probability that the sample mean will lie below £4760 if a random sample of 25 days receipts are chosen for a thorough audit?
b) What is the probability that the total receipts for 100 days will be more than £508,300?
Q2: A machine produces components in batches of 20000. At the beginning of production, the machine is set to produce the required mean length of components at 30mm and then be set to give any of 3 standard deviations:
Setting 1 0.12 mm - cost of this setting S.D. = £850
Setting 2 0.15 mm - cost of setting this standard deviation = £550
Setting 3 0.18 mm - Cost of setting this S.D. = £100
Any length produced must lie between 29.65mm and 30.41 mm, otherwise it is classed as defective and costs the company £1. You can assume the length of a component is Normally distributed. Which S.D. should be used if the decision is to be purely based on combined cost of setting the machine and of the defectives?
Thanks a lot
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